KILLED proof of input_XmxAvkcOya.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).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), 10 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 1313 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 1177 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) typed CpxTrs (23) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (24) CdtProblem (25) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CdtProblem (27) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CpxRelTRS (29) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (30) CpxTRS (31) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CpxWeightedTrs (33) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CpxTypedWeightedTrs (35) CompletionProof [UPPER BOUND(ID), 0 ms] (36) CpxTypedWeightedCompleteTrs (37) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CpxTypedWeightedCompleteTrs (39) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (40) CpxRNTS (41) InliningProof [UPPER BOUND(ID), 407 ms] (42) CpxRNTS (43) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CpxRNTS (45) CompletionProof [UPPER BOUND(ID), 0 ms] (46) CpxTypedWeightedCompleteTrs (47) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (48) CpxRNTS (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms] (62) CdtProblem (63) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtNarrowingProof [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) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtNarrowingProof [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) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [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) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 1 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5 ms] (106) CdtProblem (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 47 ms] (110) CdtProblem (111) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 32 ms] (114) CdtProblem (115) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 95 ms] (118) CdtProblem (119) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 77 ms] (122) CdtProblem (123) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 87 ms] (126) CdtProblem (127) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 89 ms] (130) CdtProblem (131) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 108 ms] (134) CdtProblem (135) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 133 ms] (138) CdtProblem (139) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 131 ms] (142) CdtProblem (143) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 169 ms] (146) CdtProblem (147) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 193 ms] (150) CdtProblem (151) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 215 ms] (154) CdtProblem (155) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 139 ms] (158) CdtProblem (159) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 125 ms] (162) CdtProblem (163) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (164) CdtProblem (165) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 3 ms] (170) CdtProblem (171) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (172) CdtProblem (173) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (174) CdtProblem (175) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 15 ms] (176) CdtProblem (177) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 41 ms] (178) CdtProblem (179) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 26 ms] (180) CdtProblem (181) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 194 ms] (182) CdtProblem (183) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 69 ms] (184) CdtProblem (185) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 353 ms] (186) CdtProblem (187) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 75 ms] (188) CdtProblem (189) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 1354 ms] (190) CdtProblem (191) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 3358 ms] (192) CdtProblem (193) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (194) CpxWeightedTrs (195) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (196) CpxTypedWeightedTrs (197) CompletionProof [UPPER BOUND(ID), 0 ms] (198) CpxTypedWeightedCompleteTrs (199) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (200) CpxRNTS (201) CompletionProof [UPPER BOUND(ID), 0 ms] (202) CpxTypedWeightedCompleteTrs (203) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (204) CpxTypedWeightedCompleteTrs (205) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (206) CpxRNTS (207) InliningProof [UPPER BOUND(ID), 233 ms] (208) CpxRNTS (209) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (210) CpxRNTS ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__zeros -> cons(0, zeros) a__and(tt, X) -> mark(X) a__length(nil) -> 0 a__length(cons(N, L)) -> s(a__length(mark(L))) mark(zeros) -> a__zeros mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(X)) -> s(mark(X)) a__zeros -> zeros a__and(X1, X2) -> and(X1, X2) a__length(X) -> length(X) 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__zeros -> cons(0', zeros) a__and(tt, X) -> mark(X) a__length(nil) -> 0' a__length(cons(N, L)) -> s(a__length(mark(L))) mark(zeros) -> a__zeros mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0') -> 0' mark(tt) -> tt mark(nil) -> nil mark(s(X)) -> s(mark(X)) a__zeros -> zeros a__and(X1, X2) -> and(X1, X2) a__length(X) -> length(X) 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__zeros -> cons(0, zeros) a__and(tt, X) -> mark(X) a__length(nil) -> 0 a__length(cons(N, L)) -> s(a__length(mark(L))) mark(zeros) -> a__zeros mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(X)) -> s(mark(X)) a__zeros -> zeros a__and(X1, X2) -> and(X1, X2) a__length(X) -> length(X) 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__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__ZEROS -> c A__ZEROS -> c1 A__AND(tt, z0) -> c2(MARK(z0)) A__AND(z0, z1) -> c3 A__LENGTH(nil) -> c4 A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) A__LENGTH(z0) -> c6 MARK(zeros) -> c7(A__ZEROS) MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(0) -> c11 MARK(tt) -> c12 MARK(nil) -> c13 MARK(s(z0)) -> c14(MARK(z0)) S tuples: A__ZEROS -> c A__ZEROS -> c1 A__AND(tt, z0) -> c2(MARK(z0)) A__AND(z0, z1) -> c3 A__LENGTH(nil) -> c4 A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) A__LENGTH(z0) -> c6 MARK(zeros) -> c7(A__ZEROS) MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(0) -> c11 MARK(tt) -> c12 MARK(nil) -> c13 MARK(s(z0)) -> c14(MARK(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__ZEROS, A__AND_2, A__LENGTH_1, MARK_1 Compound Symbols: c, c1, c2_1, c3, c4, c5_2, c6, c7_1, c8_2, c9_2, c10_1, c11, c12, c13, c14_1 ---------------------------------------- (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(n^1, INF). The TRS R consists of the following rules: A__ZEROS -> c A__ZEROS -> c1 A__AND(tt, z0) -> c2(MARK(z0)) A__AND(z0, z1) -> c3 A__LENGTH(nil) -> c4 A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) A__LENGTH(z0) -> c6 MARK(zeros) -> c7(A__ZEROS) MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(0) -> c11 MARK(tt) -> c12 MARK(nil) -> c13 MARK(s(z0)) -> c14(MARK(z0)) The (relative) TRS S consists of the following rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) 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(n^1, INF). The TRS R consists of the following rules: A__ZEROS -> c A__ZEROS -> c1 A__AND(tt, z0) -> c2(MARK(z0)) A__AND(z0, z1) -> c3 A__LENGTH(nil) -> c4 A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) A__LENGTH(z0) -> c6 MARK(zeros) -> c7(A__ZEROS) MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(0') -> c11 MARK(tt) -> c12 MARK(nil) -> c13 MARK(s(z0)) -> c14(MARK(z0)) The (relative) TRS S consists of the following rules: a__zeros -> cons(0', zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0' a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Rewrite Strategy: INNERMOST ---------------------------------------- (11) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Inferred types. ---------------------------------------- (12) Obligation: Innermost TRS: Rules: A__ZEROS -> c A__ZEROS -> c1 A__AND(tt, z0) -> c2(MARK(z0)) A__AND(z0, z1) -> c3 A__LENGTH(nil) -> c4 A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) A__LENGTH(z0) -> c6 MARK(zeros) -> c7(A__ZEROS) MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(0') -> c11 MARK(tt) -> c12 MARK(nil) -> c13 MARK(s(z0)) -> c14(MARK(z0)) a__zeros -> cons(0', zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0' a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Types: A__ZEROS :: c:c1 c :: c:c1 c1 :: c:c1 A__AND :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s -> c2:c3 tt :: tt:nil:cons:zeros:and:length:0':s c2 :: c7:c8:c9:c10:c11:c12:c13:c14 -> c2:c3 MARK :: tt:nil:cons:zeros:and:length:0':s -> c7:c8:c9:c10:c11:c12:c13:c14 c3 :: c2:c3 A__LENGTH :: tt:nil:cons:zeros:and:length:0':s -> c4:c5:c6 nil :: tt:nil:cons:zeros:and:length:0':s c4 :: c4:c5:c6 cons :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c5 :: c4:c5:c6 -> c7:c8:c9:c10:c11:c12:c13:c14 -> c4:c5:c6 mark :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c6 :: c4:c5:c6 zeros :: tt:nil:cons:zeros:and:length:0':s c7 :: c:c1 -> c7:c8:c9:c10:c11:c12:c13:c14 and :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c8 :: c2:c3 -> c7:c8:c9:c10:c11:c12:c13:c14 -> c7:c8:c9:c10:c11:c12:c13:c14 length :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c9 :: c4:c5:c6 -> c7:c8:c9:c10:c11:c12:c13:c14 -> c7:c8:c9:c10:c11:c12:c13:c14 c10 :: c7:c8:c9:c10:c11:c12:c13:c14 -> c7:c8:c9:c10:c11:c12:c13:c14 0' :: tt:nil:cons:zeros:and:length:0':s c11 :: c7:c8:c9:c10:c11:c12:c13:c14 c12 :: c7:c8:c9:c10:c11:c12:c13:c14 c13 :: c7:c8:c9:c10:c11:c12:c13:c14 s :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c14 :: c7:c8:c9:c10:c11:c12:c13:c14 -> c7:c8:c9:c10:c11:c12:c13:c14 a__zeros :: tt:nil:cons:zeros:and:length:0':s a__and :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s a__length :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s hole_c:c11_15 :: c:c1 hole_c2:c32_15 :: c2:c3 hole_tt:nil:cons:zeros:and:length:0':s3_15 :: tt:nil:cons:zeros:and:length:0':s hole_c7:c8:c9:c10:c11:c12:c13:c144_15 :: c7:c8:c9:c10:c11:c12:c13:c14 hole_c4:c5:c65_15 :: c4:c5:c6 gen_tt:nil:cons:zeros:and:length:0':s6_15 :: Nat -> tt:nil:cons:zeros:and:length:0':s gen_c7:c8:c9:c10:c11:c12:c13:c147_15 :: Nat -> c7:c8:c9:c10:c11:c12:c13:c14 gen_c4:c5:c68_15 :: Nat -> c4:c5:c6 ---------------------------------------- (13) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: MARK, A__LENGTH, mark, a__length They will be analysed ascendingly in the following order: MARK = A__LENGTH mark < MARK mark < A__LENGTH mark = a__length ---------------------------------------- (14) Obligation: Innermost TRS: Rules: A__ZEROS -> c A__ZEROS -> c1 A__AND(tt, z0) -> c2(MARK(z0)) A__AND(z0, z1) -> c3 A__LENGTH(nil) -> c4 A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) A__LENGTH(z0) -> c6 MARK(zeros) -> c7(A__ZEROS) MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(0') -> c11 MARK(tt) -> c12 MARK(nil) -> c13 MARK(s(z0)) -> c14(MARK(z0)) a__zeros -> cons(0', zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0' a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Types: A__ZEROS :: c:c1 c :: c:c1 c1 :: c:c1 A__AND :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s -> c2:c3 tt :: tt:nil:cons:zeros:and:length:0':s c2 :: c7:c8:c9:c10:c11:c12:c13:c14 -> c2:c3 MARK :: tt:nil:cons:zeros:and:length:0':s -> c7:c8:c9:c10:c11:c12:c13:c14 c3 :: c2:c3 A__LENGTH :: tt:nil:cons:zeros:and:length:0':s -> c4:c5:c6 nil :: tt:nil:cons:zeros:and:length:0':s c4 :: c4:c5:c6 cons :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c5 :: c4:c5:c6 -> c7:c8:c9:c10:c11:c12:c13:c14 -> c4:c5:c6 mark :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c6 :: c4:c5:c6 zeros :: tt:nil:cons:zeros:and:length:0':s c7 :: c:c1 -> c7:c8:c9:c10:c11:c12:c13:c14 and :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c8 :: c2:c3 -> c7:c8:c9:c10:c11:c12:c13:c14 -> c7:c8:c9:c10:c11:c12:c13:c14 length :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c9 :: c4:c5:c6 -> c7:c8:c9:c10:c11:c12:c13:c14 -> c7:c8:c9:c10:c11:c12:c13:c14 c10 :: c7:c8:c9:c10:c11:c12:c13:c14 -> c7:c8:c9:c10:c11:c12:c13:c14 0' :: tt:nil:cons:zeros:and:length:0':s c11 :: c7:c8:c9:c10:c11:c12:c13:c14 c12 :: c7:c8:c9:c10:c11:c12:c13:c14 c13 :: c7:c8:c9:c10:c11:c12:c13:c14 s :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c14 :: c7:c8:c9:c10:c11:c12:c13:c14 -> c7:c8:c9:c10:c11:c12:c13:c14 a__zeros :: tt:nil:cons:zeros:and:length:0':s a__and :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s a__length :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s hole_c:c11_15 :: c:c1 hole_c2:c32_15 :: c2:c3 hole_tt:nil:cons:zeros:and:length:0':s3_15 :: tt:nil:cons:zeros:and:length:0':s hole_c7:c8:c9:c10:c11:c12:c13:c144_15 :: c7:c8:c9:c10:c11:c12:c13:c14 hole_c4:c5:c65_15 :: c4:c5:c6 gen_tt:nil:cons:zeros:and:length:0':s6_15 :: Nat -> tt:nil:cons:zeros:and:length:0':s gen_c7:c8:c9:c10:c11:c12:c13:c147_15 :: Nat -> c7:c8:c9:c10:c11:c12:c13:c14 gen_c4:c5:c68_15 :: Nat -> c4:c5:c6 Generator Equations: gen_tt:nil:cons:zeros:and:length:0':s6_15(0) <=> tt gen_tt:nil:cons:zeros:and:length:0':s6_15(+(x, 1)) <=> cons(tt, gen_tt:nil:cons:zeros:and:length:0':s6_15(x)) gen_c7:c8:c9:c10:c11:c12:c13:c147_15(0) <=> c7(c) gen_c7:c8:c9:c10:c11:c12:c13:c147_15(+(x, 1)) <=> c8(c2(c7(c)), gen_c7:c8:c9:c10:c11:c12:c13:c147_15(x)) gen_c4:c5:c68_15(0) <=> c4 gen_c4:c5:c68_15(+(x, 1)) <=> c5(gen_c4:c5:c68_15(x), c7(c)) The following defined symbols remain to be analysed: a__length, MARK, A__LENGTH, mark They will be analysed ascendingly in the following order: MARK = A__LENGTH mark < MARK mark < A__LENGTH mark = a__length ---------------------------------------- (15) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: a__length(gen_tt:nil:cons:zeros:and:length:0':s6_15(+(1, n10_15))) -> *9_15, rt in Omega(0) Induction Base: a__length(gen_tt:nil:cons:zeros:and:length:0':s6_15(+(1, 0))) Induction Step: a__length(gen_tt:nil:cons:zeros:and:length:0':s6_15(+(1, +(n10_15, 1)))) ->_R^Omega(0) s(a__length(mark(gen_tt:nil:cons:zeros:and:length:0':s6_15(+(1, n10_15))))) ->_R^Omega(0) s(a__length(cons(mark(tt), gen_tt:nil:cons:zeros:and:length:0':s6_15(n10_15)))) ->_R^Omega(0) s(a__length(cons(tt, gen_tt:nil:cons:zeros:and:length:0':s6_15(n10_15)))) ->_IH s(*9_15) 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__ZEROS -> c A__ZEROS -> c1 A__AND(tt, z0) -> c2(MARK(z0)) A__AND(z0, z1) -> c3 A__LENGTH(nil) -> c4 A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) A__LENGTH(z0) -> c6 MARK(zeros) -> c7(A__ZEROS) MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(0') -> c11 MARK(tt) -> c12 MARK(nil) -> c13 MARK(s(z0)) -> c14(MARK(z0)) a__zeros -> cons(0', zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0' a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Types: A__ZEROS :: c:c1 c :: c:c1 c1 :: c:c1 A__AND :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s -> c2:c3 tt :: tt:nil:cons:zeros:and:length:0':s c2 :: c7:c8:c9:c10:c11:c12:c13:c14 -> c2:c3 MARK :: tt:nil:cons:zeros:and:length:0':s -> c7:c8:c9:c10:c11:c12:c13:c14 c3 :: c2:c3 A__LENGTH :: tt:nil:cons:zeros:and:length:0':s -> c4:c5:c6 nil :: tt:nil:cons:zeros:and:length:0':s c4 :: c4:c5:c6 cons :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c5 :: c4:c5:c6 -> c7:c8:c9:c10:c11:c12:c13:c14 -> c4:c5:c6 mark :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c6 :: c4:c5:c6 zeros :: tt:nil:cons:zeros:and:length:0':s c7 :: c:c1 -> c7:c8:c9:c10:c11:c12:c13:c14 and :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c8 :: c2:c3 -> c7:c8:c9:c10:c11:c12:c13:c14 -> c7:c8:c9:c10:c11:c12:c13:c14 length :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c9 :: c4:c5:c6 -> c7:c8:c9:c10:c11:c12:c13:c14 -> c7:c8:c9:c10:c11:c12:c13:c14 c10 :: c7:c8:c9:c10:c11:c12:c13:c14 -> c7:c8:c9:c10:c11:c12:c13:c14 0' :: tt:nil:cons:zeros:and:length:0':s c11 :: c7:c8:c9:c10:c11:c12:c13:c14 c12 :: c7:c8:c9:c10:c11:c12:c13:c14 c13 :: c7:c8:c9:c10:c11:c12:c13:c14 s :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c14 :: c7:c8:c9:c10:c11:c12:c13:c14 -> c7:c8:c9:c10:c11:c12:c13:c14 a__zeros :: tt:nil:cons:zeros:and:length:0':s a__and :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s a__length :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s hole_c:c11_15 :: c:c1 hole_c2:c32_15 :: c2:c3 hole_tt:nil:cons:zeros:and:length:0':s3_15 :: tt:nil:cons:zeros:and:length:0':s hole_c7:c8:c9:c10:c11:c12:c13:c144_15 :: c7:c8:c9:c10:c11:c12:c13:c14 hole_c4:c5:c65_15 :: c4:c5:c6 gen_tt:nil:cons:zeros:and:length:0':s6_15 :: Nat -> tt:nil:cons:zeros:and:length:0':s gen_c7:c8:c9:c10:c11:c12:c13:c147_15 :: Nat -> c7:c8:c9:c10:c11:c12:c13:c14 gen_c4:c5:c68_15 :: Nat -> c4:c5:c6 Lemmas: a__length(gen_tt:nil:cons:zeros:and:length:0':s6_15(+(1, n10_15))) -> *9_15, rt in Omega(0) Generator Equations: gen_tt:nil:cons:zeros:and:length:0':s6_15(0) <=> tt gen_tt:nil:cons:zeros:and:length:0':s6_15(+(x, 1)) <=> cons(tt, gen_tt:nil:cons:zeros:and:length:0':s6_15(x)) gen_c7:c8:c9:c10:c11:c12:c13:c147_15(0) <=> c7(c) gen_c7:c8:c9:c10:c11:c12:c13:c147_15(+(x, 1)) <=> c8(c2(c7(c)), gen_c7:c8:c9:c10:c11:c12:c13:c147_15(x)) gen_c4:c5:c68_15(0) <=> c4 gen_c4:c5:c68_15(+(x, 1)) <=> c5(gen_c4:c5:c68_15(x), c7(c)) The following defined symbols remain to be analysed: mark, MARK, A__LENGTH They will be analysed ascendingly in the following order: MARK = A__LENGTH mark < MARK mark < A__LENGTH mark = a__length ---------------------------------------- (17) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: A__LENGTH(gen_tt:nil:cons:zeros:and:length:0':s6_15(+(1, n18015_15))) -> *9_15, rt in Omega(n18015_15) Induction Base: A__LENGTH(gen_tt:nil:cons:zeros:and:length:0':s6_15(+(1, 0))) Induction Step: A__LENGTH(gen_tt:nil:cons:zeros:and:length:0':s6_15(+(1, +(n18015_15, 1)))) ->_R^Omega(1) c5(A__LENGTH(mark(gen_tt:nil:cons:zeros:and:length:0':s6_15(+(1, n18015_15)))), MARK(gen_tt:nil:cons:zeros:and:length:0':s6_15(+(1, n18015_15)))) ->_R^Omega(0) c5(A__LENGTH(cons(mark(tt), gen_tt:nil:cons:zeros:and:length:0':s6_15(n18015_15))), MARK(gen_tt:nil:cons:zeros:and:length:0':s6_15(+(1, n18015_15)))) ->_R^Omega(0) c5(A__LENGTH(cons(tt, gen_tt:nil:cons:zeros:and:length:0':s6_15(n18015_15))), MARK(gen_tt:nil:cons:zeros:and:length:0':s6_15(+(1, n18015_15)))) ->_IH c5(*9_15, MARK(gen_tt:nil:cons:zeros:and:length:0':s6_15(+(1, n18015_15)))) ->_R^Omega(1) c5(*9_15, c10(MARK(tt))) ->_R^Omega(1) c5(*9_15, c10(c12)) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (18) Complex Obligation (BEST) ---------------------------------------- (19) Obligation: Proved the lower bound n^1 for the following obligation: Innermost TRS: Rules: A__ZEROS -> c A__ZEROS -> c1 A__AND(tt, z0) -> c2(MARK(z0)) A__AND(z0, z1) -> c3 A__LENGTH(nil) -> c4 A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) A__LENGTH(z0) -> c6 MARK(zeros) -> c7(A__ZEROS) MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(0') -> c11 MARK(tt) -> c12 MARK(nil) -> c13 MARK(s(z0)) -> c14(MARK(z0)) a__zeros -> cons(0', zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0' a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Types: A__ZEROS :: c:c1 c :: c:c1 c1 :: c:c1 A__AND :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s -> c2:c3 tt :: tt:nil:cons:zeros:and:length:0':s c2 :: c7:c8:c9:c10:c11:c12:c13:c14 -> c2:c3 MARK :: tt:nil:cons:zeros:and:length:0':s -> c7:c8:c9:c10:c11:c12:c13:c14 c3 :: c2:c3 A__LENGTH :: tt:nil:cons:zeros:and:length:0':s -> c4:c5:c6 nil :: tt:nil:cons:zeros:and:length:0':s c4 :: c4:c5:c6 cons :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c5 :: c4:c5:c6 -> c7:c8:c9:c10:c11:c12:c13:c14 -> c4:c5:c6 mark :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c6 :: c4:c5:c6 zeros :: tt:nil:cons:zeros:and:length:0':s c7 :: c:c1 -> c7:c8:c9:c10:c11:c12:c13:c14 and :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c8 :: c2:c3 -> c7:c8:c9:c10:c11:c12:c13:c14 -> c7:c8:c9:c10:c11:c12:c13:c14 length :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c9 :: c4:c5:c6 -> c7:c8:c9:c10:c11:c12:c13:c14 -> c7:c8:c9:c10:c11:c12:c13:c14 c10 :: c7:c8:c9:c10:c11:c12:c13:c14 -> c7:c8:c9:c10:c11:c12:c13:c14 0' :: tt:nil:cons:zeros:and:length:0':s c11 :: c7:c8:c9:c10:c11:c12:c13:c14 c12 :: c7:c8:c9:c10:c11:c12:c13:c14 c13 :: c7:c8:c9:c10:c11:c12:c13:c14 s :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c14 :: c7:c8:c9:c10:c11:c12:c13:c14 -> c7:c8:c9:c10:c11:c12:c13:c14 a__zeros :: tt:nil:cons:zeros:and:length:0':s a__and :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s a__length :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s hole_c:c11_15 :: c:c1 hole_c2:c32_15 :: c2:c3 hole_tt:nil:cons:zeros:and:length:0':s3_15 :: tt:nil:cons:zeros:and:length:0':s hole_c7:c8:c9:c10:c11:c12:c13:c144_15 :: c7:c8:c9:c10:c11:c12:c13:c14 hole_c4:c5:c65_15 :: c4:c5:c6 gen_tt:nil:cons:zeros:and:length:0':s6_15 :: Nat -> tt:nil:cons:zeros:and:length:0':s gen_c7:c8:c9:c10:c11:c12:c13:c147_15 :: Nat -> c7:c8:c9:c10:c11:c12:c13:c14 gen_c4:c5:c68_15 :: Nat -> c4:c5:c6 Lemmas: a__length(gen_tt:nil:cons:zeros:and:length:0':s6_15(+(1, n10_15))) -> *9_15, rt in Omega(0) Generator Equations: gen_tt:nil:cons:zeros:and:length:0':s6_15(0) <=> tt gen_tt:nil:cons:zeros:and:length:0':s6_15(+(x, 1)) <=> cons(tt, gen_tt:nil:cons:zeros:and:length:0':s6_15(x)) gen_c7:c8:c9:c10:c11:c12:c13:c147_15(0) <=> c7(c) gen_c7:c8:c9:c10:c11:c12:c13:c147_15(+(x, 1)) <=> c8(c2(c7(c)), gen_c7:c8:c9:c10:c11:c12:c13:c147_15(x)) gen_c4:c5:c68_15(0) <=> c4 gen_c4:c5:c68_15(+(x, 1)) <=> c5(gen_c4:c5:c68_15(x), c7(c)) The following defined symbols remain to be analysed: A__LENGTH, MARK They will be analysed ascendingly in the following order: MARK = A__LENGTH ---------------------------------------- (20) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (21) BOUNDS(n^1, INF) ---------------------------------------- (22) Obligation: Innermost TRS: Rules: A__ZEROS -> c A__ZEROS -> c1 A__AND(tt, z0) -> c2(MARK(z0)) A__AND(z0, z1) -> c3 A__LENGTH(nil) -> c4 A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) A__LENGTH(z0) -> c6 MARK(zeros) -> c7(A__ZEROS) MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(0') -> c11 MARK(tt) -> c12 MARK(nil) -> c13 MARK(s(z0)) -> c14(MARK(z0)) a__zeros -> cons(0', zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0' a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Types: A__ZEROS :: c:c1 c :: c:c1 c1 :: c:c1 A__AND :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s -> c2:c3 tt :: tt:nil:cons:zeros:and:length:0':s c2 :: c7:c8:c9:c10:c11:c12:c13:c14 -> c2:c3 MARK :: tt:nil:cons:zeros:and:length:0':s -> c7:c8:c9:c10:c11:c12:c13:c14 c3 :: c2:c3 A__LENGTH :: tt:nil:cons:zeros:and:length:0':s -> c4:c5:c6 nil :: tt:nil:cons:zeros:and:length:0':s c4 :: c4:c5:c6 cons :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c5 :: c4:c5:c6 -> c7:c8:c9:c10:c11:c12:c13:c14 -> c4:c5:c6 mark :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c6 :: c4:c5:c6 zeros :: tt:nil:cons:zeros:and:length:0':s c7 :: c:c1 -> c7:c8:c9:c10:c11:c12:c13:c14 and :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c8 :: c2:c3 -> c7:c8:c9:c10:c11:c12:c13:c14 -> c7:c8:c9:c10:c11:c12:c13:c14 length :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c9 :: c4:c5:c6 -> c7:c8:c9:c10:c11:c12:c13:c14 -> c7:c8:c9:c10:c11:c12:c13:c14 c10 :: c7:c8:c9:c10:c11:c12:c13:c14 -> c7:c8:c9:c10:c11:c12:c13:c14 0' :: tt:nil:cons:zeros:and:length:0':s c11 :: c7:c8:c9:c10:c11:c12:c13:c14 c12 :: c7:c8:c9:c10:c11:c12:c13:c14 c13 :: c7:c8:c9:c10:c11:c12:c13:c14 s :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s c14 :: c7:c8:c9:c10:c11:c12:c13:c14 -> c7:c8:c9:c10:c11:c12:c13:c14 a__zeros :: tt:nil:cons:zeros:and:length:0':s a__and :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s a__length :: tt:nil:cons:zeros:and:length:0':s -> tt:nil:cons:zeros:and:length:0':s hole_c:c11_15 :: c:c1 hole_c2:c32_15 :: c2:c3 hole_tt:nil:cons:zeros:and:length:0':s3_15 :: tt:nil:cons:zeros:and:length:0':s hole_c7:c8:c9:c10:c11:c12:c13:c144_15 :: c7:c8:c9:c10:c11:c12:c13:c14 hole_c4:c5:c65_15 :: c4:c5:c6 gen_tt:nil:cons:zeros:and:length:0':s6_15 :: Nat -> tt:nil:cons:zeros:and:length:0':s gen_c7:c8:c9:c10:c11:c12:c13:c147_15 :: Nat -> c7:c8:c9:c10:c11:c12:c13:c14 gen_c4:c5:c68_15 :: Nat -> c4:c5:c6 Lemmas: a__length(gen_tt:nil:cons:zeros:and:length:0':s6_15(+(1, n10_15))) -> *9_15, rt in Omega(0) A__LENGTH(gen_tt:nil:cons:zeros:and:length:0':s6_15(+(1, n18015_15))) -> *9_15, rt in Omega(n18015_15) Generator Equations: gen_tt:nil:cons:zeros:and:length:0':s6_15(0) <=> tt gen_tt:nil:cons:zeros:and:length:0':s6_15(+(x, 1)) <=> cons(tt, gen_tt:nil:cons:zeros:and:length:0':s6_15(x)) gen_c7:c8:c9:c10:c11:c12:c13:c147_15(0) <=> c7(c) gen_c7:c8:c9:c10:c11:c12:c13:c147_15(+(x, 1)) <=> c8(c2(c7(c)), gen_c7:c8:c9:c10:c11:c12:c13:c147_15(x)) gen_c4:c5:c68_15(0) <=> c4 gen_c4:c5:c68_15(+(x, 1)) <=> c5(gen_c4:c5:c68_15(x), c7(c)) The following defined symbols remain to be analysed: MARK They will be analysed ascendingly in the following order: MARK = A__LENGTH ---------------------------------------- (23) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (24) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__ZEROS -> c A__ZEROS -> c1 A__AND(tt, z0) -> c2(MARK(z0)) A__AND(z0, z1) -> c3 A__LENGTH(nil) -> c4 A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) A__LENGTH(z0) -> c6 MARK(zeros) -> c7(A__ZEROS) MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(0) -> c11 MARK(tt) -> c12 MARK(nil) -> c13 MARK(s(z0)) -> c14(MARK(z0)) S tuples: A__ZEROS -> c A__ZEROS -> c1 A__AND(tt, z0) -> c2(MARK(z0)) A__AND(z0, z1) -> c3 A__LENGTH(nil) -> c4 A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) A__LENGTH(z0) -> c6 MARK(zeros) -> c7(A__ZEROS) MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(0) -> c11 MARK(tt) -> c12 MARK(nil) -> c13 MARK(s(z0)) -> c14(MARK(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__ZEROS, A__AND_2, A__LENGTH_1, MARK_1 Compound Symbols: c, c1, c2_1, c3, c4, c5_2, c6, c7_1, c8_2, c9_2, c10_1, c11, c12, c13, c14_1 ---------------------------------------- (25) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 9 trailing nodes: MARK(zeros) -> c7(A__ZEROS) MARK(tt) -> c12 A__ZEROS -> c A__AND(z0, z1) -> c3 A__LENGTH(z0) -> c6 MARK(0) -> c11 A__LENGTH(nil) -> c4 A__ZEROS -> c1 MARK(nil) -> c13 ---------------------------------------- (26) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, A__LENGTH_1, MARK_1 Compound Symbols: c2_1, c5_2, c8_2, c9_2, c10_1, c14_1 ---------------------------------------- (27) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (28) 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__AND(tt, z0) -> c2(MARK(z0)) A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) The (relative) TRS S consists of the following rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Rewrite Strategy: INNERMOST ---------------------------------------- (29) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (30) 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__AND(tt, z0) -> c2(MARK(z0)) A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (31) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (32) 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__AND(tt, z0) -> c2(MARK(z0)) [1] A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) [1] MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) [1] MARK(cons(z0, z1)) -> c10(MARK(z0)) [1] MARK(s(z0)) -> c14(MARK(z0)) [1] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__and(tt, z0) -> mark(z0) [0] a__and(z0, z1) -> and(z0, z1) [0] a__length(nil) -> 0 [0] a__length(cons(z0, z1)) -> s(a__length(mark(z1))) [0] a__length(z0) -> length(z0) [0] mark(zeros) -> a__zeros [0] mark(and(z0, z1)) -> a__and(mark(z0), z1) [0] mark(length(z0)) -> a__length(mark(z0)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(tt) -> tt [0] mark(nil) -> nil [0] mark(s(z0)) -> s(mark(z0)) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (33) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (34) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__AND(tt, z0) -> c2(MARK(z0)) [1] A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) [1] MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) [1] MARK(cons(z0, z1)) -> c10(MARK(z0)) [1] MARK(s(z0)) -> c14(MARK(z0)) [1] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__and(tt, z0) -> mark(z0) [0] a__and(z0, z1) -> and(z0, z1) [0] a__length(nil) -> 0 [0] a__length(cons(z0, z1)) -> s(a__length(mark(z1))) [0] a__length(z0) -> length(z0) [0] mark(zeros) -> a__zeros [0] mark(and(z0, z1)) -> a__and(mark(z0), z1) [0] mark(length(z0)) -> a__length(mark(z0)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(tt) -> tt [0] mark(nil) -> nil [0] mark(s(z0)) -> s(mark(z0)) [0] The TRS has the following type information: A__AND :: tt:cons:and:length:s:0:zeros:nil -> tt:cons:and:length:s:0:zeros:nil -> c2 tt :: tt:cons:and:length:s:0:zeros:nil c2 :: c8:c9:c10:c14 -> c2 MARK :: tt:cons:and:length:s:0:zeros:nil -> c8:c9:c10:c14 A__LENGTH :: tt:cons:and:length:s:0:zeros:nil -> c5 cons :: tt:cons:and:length:s:0:zeros:nil -> tt:cons:and:length:s:0:zeros:nil -> tt:cons:and:length:s:0:zeros:nil c5 :: c5 -> c8:c9:c10:c14 -> c5 mark :: tt:cons:and:length:s:0:zeros:nil -> tt:cons:and:length:s:0:zeros:nil and :: tt:cons:and:length:s:0:zeros:nil -> tt:cons:and:length:s:0:zeros:nil -> tt:cons:and:length:s:0:zeros:nil c8 :: c2 -> c8:c9:c10:c14 -> c8:c9:c10:c14 length :: tt:cons:and:length:s:0:zeros:nil -> tt:cons:and:length:s:0:zeros:nil c9 :: c5 -> c8:c9:c10:c14 -> c8:c9:c10:c14 c10 :: c8:c9:c10:c14 -> c8:c9:c10:c14 s :: tt:cons:and:length:s:0:zeros:nil -> tt:cons:and:length:s:0:zeros:nil c14 :: c8:c9:c10:c14 -> c8:c9:c10:c14 a__zeros :: tt:cons:and:length:s:0:zeros:nil 0 :: tt:cons:and:length:s:0:zeros:nil zeros :: tt:cons:and:length:s:0:zeros:nil a__and :: tt:cons:and:length:s:0:zeros:nil -> tt:cons:and:length:s:0:zeros:nil -> tt:cons:and:length:s:0:zeros:nil a__length :: tt:cons:and:length:s:0:zeros:nil -> tt:cons:and:length:s:0:zeros:nil nil :: tt:cons:and:length:s:0:zeros:nil Rewrite Strategy: INNERMOST ---------------------------------------- (35) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: A__AND_2 A__LENGTH_1 MARK_1 (c) The following functions are completely defined: a__zeros a__and_2 a__length_1 mark_1 Due to the following rules being added: a__zeros -> null_a__zeros [0] a__and(v0, v1) -> null_a__and [0] a__length(v0) -> null_a__length [0] mark(v0) -> null_mark [0] And the following fresh constants: null_a__zeros, null_a__and, null_a__length, null_mark, const, const1, const2 ---------------------------------------- (36) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__AND(tt, z0) -> c2(MARK(z0)) [1] A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) [1] MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) [1] MARK(cons(z0, z1)) -> c10(MARK(z0)) [1] MARK(s(z0)) -> c14(MARK(z0)) [1] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__and(tt, z0) -> mark(z0) [0] a__and(z0, z1) -> and(z0, z1) [0] a__length(nil) -> 0 [0] a__length(cons(z0, z1)) -> s(a__length(mark(z1))) [0] a__length(z0) -> length(z0) [0] mark(zeros) -> a__zeros [0] mark(and(z0, z1)) -> a__and(mark(z0), z1) [0] mark(length(z0)) -> a__length(mark(z0)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(tt) -> tt [0] mark(nil) -> nil [0] mark(s(z0)) -> s(mark(z0)) [0] a__zeros -> null_a__zeros [0] a__and(v0, v1) -> null_a__and [0] a__length(v0) -> null_a__length [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__AND :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> c2 tt :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark c2 :: c8:c9:c10:c14 -> c2 MARK :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> c8:c9:c10:c14 A__LENGTH :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> c5 cons :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark c5 :: c5 -> c8:c9:c10:c14 -> c5 mark :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark and :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark c8 :: c2 -> c8:c9:c10:c14 -> c8:c9:c10:c14 length :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark c9 :: c5 -> c8:c9:c10:c14 -> c8:c9:c10:c14 c10 :: c8:c9:c10:c14 -> c8:c9:c10:c14 s :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark c14 :: c8:c9:c10:c14 -> c8:c9:c10:c14 a__zeros :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark 0 :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark zeros :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark a__and :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark a__length :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark nil :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark null_a__zeros :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark null_a__and :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark null_a__length :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark null_mark :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark const :: c2 const1 :: c8:c9:c10:c14 const2 :: c5 Rewrite Strategy: INNERMOST ---------------------------------------- (37) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (38) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__AND(tt, z0) -> c2(MARK(z0)) [1] A__LENGTH(cons(z0, zeros)) -> c5(A__LENGTH(a__zeros), MARK(zeros)) [1] A__LENGTH(cons(z0, and(z0', z1'))) -> c5(A__LENGTH(a__and(mark(z0'), z1')), MARK(and(z0', z1'))) [1] A__LENGTH(cons(z0, length(z0''))) -> c5(A__LENGTH(a__length(mark(z0''))), MARK(length(z0''))) [1] A__LENGTH(cons(z0, cons(z01, z1''))) -> c5(A__LENGTH(cons(mark(z01), z1'')), MARK(cons(z01, z1''))) [1] A__LENGTH(cons(z0, 0)) -> c5(A__LENGTH(0), MARK(0)) [1] A__LENGTH(cons(z0, tt)) -> c5(A__LENGTH(tt), MARK(tt)) [1] A__LENGTH(cons(z0, nil)) -> c5(A__LENGTH(nil), MARK(nil)) [1] A__LENGTH(cons(z0, s(z02))) -> c5(A__LENGTH(s(mark(z02))), MARK(s(z02))) [1] A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(null_mark), MARK(z1)) [1] MARK(and(zeros, z1)) -> c8(A__AND(a__zeros, z1), MARK(zeros)) [1] MARK(and(and(z03, z11), z1)) -> c8(A__AND(a__and(mark(z03), z11), z1), MARK(and(z03, z11))) [1] MARK(and(length(z04), z1)) -> c8(A__AND(a__length(mark(z04)), z1), MARK(length(z04))) [1] MARK(and(cons(z05, z12), z1)) -> c8(A__AND(cons(mark(z05), z12), z1), MARK(cons(z05, z12))) [1] MARK(and(0, z1)) -> c8(A__AND(0, z1), MARK(0)) [1] MARK(and(tt, z1)) -> c8(A__AND(tt, z1), MARK(tt)) [1] MARK(and(nil, z1)) -> c8(A__AND(nil, z1), MARK(nil)) [1] MARK(and(s(z06), z1)) -> c8(A__AND(s(mark(z06)), z1), MARK(s(z06))) [1] MARK(and(z0, z1)) -> c8(A__AND(null_mark, z1), MARK(z0)) [1] MARK(length(zeros)) -> c9(A__LENGTH(a__zeros), MARK(zeros)) [1] MARK(length(and(z07, z13))) -> c9(A__LENGTH(a__and(mark(z07), z13)), MARK(and(z07, z13))) [1] MARK(length(length(z08))) -> c9(A__LENGTH(a__length(mark(z08))), MARK(length(z08))) [1] MARK(length(cons(z09, z14))) -> c9(A__LENGTH(cons(mark(z09), z14)), MARK(cons(z09, z14))) [1] MARK(length(0)) -> c9(A__LENGTH(0), MARK(0)) [1] MARK(length(tt)) -> c9(A__LENGTH(tt), MARK(tt)) [1] MARK(length(nil)) -> c9(A__LENGTH(nil), MARK(nil)) [1] MARK(length(s(z010))) -> c9(A__LENGTH(s(mark(z010))), MARK(s(z010))) [1] MARK(length(z0)) -> c9(A__LENGTH(null_mark), MARK(z0)) [1] MARK(cons(z0, z1)) -> c10(MARK(z0)) [1] MARK(s(z0)) -> c14(MARK(z0)) [1] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__and(tt, z0) -> mark(z0) [0] a__and(z0, z1) -> and(z0, z1) [0] a__length(nil) -> 0 [0] a__length(cons(z0, zeros)) -> s(a__length(a__zeros)) [0] a__length(cons(z0, and(z011, z15))) -> s(a__length(a__and(mark(z011), z15))) [0] a__length(cons(z0, length(z012))) -> s(a__length(a__length(mark(z012)))) [0] a__length(cons(z0, cons(z013, z16))) -> s(a__length(cons(mark(z013), z16))) [0] a__length(cons(z0, 0)) -> s(a__length(0)) [0] a__length(cons(z0, tt)) -> s(a__length(tt)) [0] a__length(cons(z0, nil)) -> s(a__length(nil)) [0] a__length(cons(z0, s(z014))) -> s(a__length(s(mark(z014)))) [0] a__length(cons(z0, z1)) -> s(a__length(null_mark)) [0] a__length(z0) -> length(z0) [0] mark(zeros) -> a__zeros [0] mark(and(zeros, z1)) -> a__and(a__zeros, z1) [0] mark(and(and(z015, z17), z1)) -> a__and(a__and(mark(z015), z17), z1) [0] mark(and(length(z016), z1)) -> a__and(a__length(mark(z016)), z1) [0] mark(and(cons(z017, z18), z1)) -> a__and(cons(mark(z017), z18), z1) [0] mark(and(0, z1)) -> a__and(0, z1) [0] mark(and(tt, z1)) -> a__and(tt, z1) [0] mark(and(nil, z1)) -> a__and(nil, z1) [0] mark(and(s(z018), z1)) -> a__and(s(mark(z018)), z1) [0] mark(and(z0, z1)) -> a__and(null_mark, z1) [0] mark(length(zeros)) -> a__length(a__zeros) [0] mark(length(and(z019, z19))) -> a__length(a__and(mark(z019), z19)) [0] mark(length(length(z020))) -> a__length(a__length(mark(z020))) [0] mark(length(cons(z021, z110))) -> a__length(cons(mark(z021), z110)) [0] mark(length(0)) -> a__length(0) [0] mark(length(tt)) -> a__length(tt) [0] mark(length(nil)) -> a__length(nil) [0] mark(length(s(z022))) -> a__length(s(mark(z022))) [0] mark(length(z0)) -> a__length(null_mark) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(tt) -> tt [0] mark(nil) -> nil [0] mark(s(z0)) -> s(mark(z0)) [0] a__zeros -> null_a__zeros [0] a__and(v0, v1) -> null_a__and [0] a__length(v0) -> null_a__length [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__AND :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> c2 tt :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark c2 :: c8:c9:c10:c14 -> c2 MARK :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> c8:c9:c10:c14 A__LENGTH :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> c5 cons :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark c5 :: c5 -> c8:c9:c10:c14 -> c5 mark :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark and :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark c8 :: c2 -> c8:c9:c10:c14 -> c8:c9:c10:c14 length :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark c9 :: c5 -> c8:c9:c10:c14 -> c8:c9:c10:c14 c10 :: c8:c9:c10:c14 -> c8:c9:c10:c14 s :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark c14 :: c8:c9:c10:c14 -> c8:c9:c10:c14 a__zeros :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark 0 :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark zeros :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark a__and :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark a__length :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark nil :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark null_a__zeros :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark null_a__and :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark null_a__length :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark null_mark :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark const :: c2 const1 :: c8:c9:c10:c14 const2 :: c5 Rewrite Strategy: INNERMOST ---------------------------------------- (39) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 2 0 => 0 zeros => 3 nil => 1 null_a__zeros => 0 null_a__and => 0 null_a__length => 0 null_mark => 0 const => 0 const1 => 0 const2 => 0 ---------------------------------------- (40) Obligation: Complexity RNTS consisting of the following rules: A__AND(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 2, z0 >= 0, z' = z0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(a__zeros) + MARK(3) :|: z = 1 + z0 + 3, z0 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(a__length(mark(z0''))) + MARK(1 + z0'') :|: z = 1 + z0 + (1 + z0''), z0 >= 0, z0'' >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(a__and(mark(z0'), z1')) + MARK(1 + z0' + z1') :|: z = 1 + z0 + (1 + z0' + z1'), z0' >= 0, z1' >= 0, z0 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(2) + MARK(2) :|: z = 1 + z0 + 2, z0 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(1) + MARK(1) :|: z0 >= 0, z = 1 + z0 + 1 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(0) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(0) + MARK(0) :|: z0 >= 0, z = 1 + z0 + 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(1 + mark(z02)) + MARK(1 + z02) :|: z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(1 + mark(z01) + z1'') + MARK(1 + z01 + z1'') :|: z = 1 + z0 + (1 + z01 + z1''), z01 >= 0, z0 >= 0, z1'' >= 0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(a__zeros) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__LENGTH(a__length(mark(z08))) + MARK(1 + z08) :|: z08 >= 0, z = 1 + (1 + z08) MARK(z) -{ 1 }-> 1 + A__LENGTH(a__and(mark(z07), z13)) + MARK(1 + z07 + z13) :|: z = 1 + (1 + z07 + z13), z07 >= 0, z13 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(2) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__LENGTH(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__LENGTH(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(1 + mark(z010)) + MARK(1 + z010) :|: z = 1 + (1 + z010), z010 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(1 + mark(z09) + z14) + MARK(1 + z09 + z14) :|: z = 1 + (1 + z09 + z14), z09 >= 0, z14 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__zeros, z1) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__length(mark(z04)), z1) + MARK(1 + z04) :|: z04 >= 0, z1 >= 0, z = 1 + (1 + z04) + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__and(mark(z03), z11), z1) + MARK(1 + z03 + z11) :|: z11 >= 0, z1 >= 0, z03 >= 0, z = 1 + (1 + z03 + z11) + z1 MARK(z) -{ 1 }-> 1 + A__AND(2, z1) + MARK(2) :|: z1 >= 0, z = 1 + 2 + z1 MARK(z) -{ 1 }-> 1 + A__AND(1, z1) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 MARK(z) -{ 1 }-> 1 + A__AND(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__AND(0, z1) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 MARK(z) -{ 1 }-> 1 + A__AND(1 + mark(z06), z1) + MARK(1 + z06) :|: z1 >= 0, z = 1 + (1 + z06) + z1, z06 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(1 + mark(z05) + z12, z1) + MARK(1 + z05 + z12) :|: z = 1 + (1 + z05 + z12) + z1, z1 >= 0, z12 >= 0, z05 >= 0 a__and(z, z') -{ 0 }-> mark(z0) :|: z = 2, z0 >= 0, z' = z0 a__and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__and(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__length(z) -{ 0 }-> 0 :|: z = 1 a__length(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__length(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__length(z) -{ 0 }-> 1 + a__length(a__zeros) :|: z = 1 + z0 + 3, z0 >= 0 a__length(z) -{ 0 }-> 1 + a__length(a__length(mark(z012))) :|: z = 1 + z0 + (1 + z012), z0 >= 0, z012 >= 0 a__length(z) -{ 0 }-> 1 + a__length(a__and(mark(z011), z15)) :|: z011 >= 0, z15 >= 0, z = 1 + z0 + (1 + z011 + z15), z0 >= 0 a__length(z) -{ 0 }-> 1 + a__length(2) :|: z = 1 + z0 + 2, z0 >= 0 a__length(z) -{ 0 }-> 1 + a__length(1) :|: z0 >= 0, z = 1 + z0 + 1 a__length(z) -{ 0 }-> 1 + a__length(0) :|: z0 >= 0, z = 1 + z0 + 0 a__length(z) -{ 0 }-> 1 + a__length(0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__length(z) -{ 0 }-> 1 + a__length(1 + mark(z014)) :|: z = 1 + z0 + (1 + z014), z014 >= 0, z0 >= 0 a__length(z) -{ 0 }-> 1 + a__length(1 + mark(z013) + z16) :|: z013 >= 0, z0 >= 0, z16 >= 0, z = 1 + z0 + (1 + z013 + z16) a__zeros -{ 0 }-> 3 :|: a__zeros -{ 0 }-> 0 :|: a__zeros -{ 0 }-> 1 + 0 + 3 :|: mark(z) -{ 0 }-> a__zeros :|: z = 3 mark(z) -{ 0 }-> a__length(a__zeros) :|: z = 1 + 3 mark(z) -{ 0 }-> a__length(a__length(mark(z020))) :|: z = 1 + (1 + z020), z020 >= 0 mark(z) -{ 0 }-> a__length(a__and(mark(z019), z19)) :|: z019 >= 0, z19 >= 0, z = 1 + (1 + z019 + z19) mark(z) -{ 0 }-> a__length(2) :|: z = 1 + 2 mark(z) -{ 0 }-> a__length(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__length(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__length(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__length(1 + mark(z022)) :|: z022 >= 0, z = 1 + (1 + z022) mark(z) -{ 0 }-> a__length(1 + mark(z021) + z110) :|: z021 >= 0, z110 >= 0, z = 1 + (1 + z021 + z110) mark(z) -{ 0 }-> a__and(a__zeros, z1) :|: z1 >= 0, z = 1 + 3 + z1 mark(z) -{ 0 }-> a__and(a__length(mark(z016)), z1) :|: z1 >= 0, z016 >= 0, z = 1 + (1 + z016) + z1 mark(z) -{ 0 }-> a__and(a__and(mark(z015), z17), z1) :|: z015 >= 0, z1 >= 0, z = 1 + (1 + z015 + z17) + z1, z17 >= 0 mark(z) -{ 0 }-> a__and(2, z1) :|: z1 >= 0, z = 1 + 2 + z1 mark(z) -{ 0 }-> a__and(1, z1) :|: z1 >= 0, z = 1 + 1 + z1 mark(z) -{ 0 }-> a__and(0, z1) :|: z1 >= 0, z = 1 + 0 + z1 mark(z) -{ 0 }-> a__and(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__and(1 + mark(z018), z1) :|: z1 >= 0, z = 1 + (1 + z018) + z1, z018 >= 0 mark(z) -{ 0 }-> a__and(1 + mark(z017) + z18, z1) :|: z18 >= 0, z1 >= 0, z = 1 + (1 + z017 + z18) + z1, z017 >= 0 mark(z) -{ 0 }-> 2 :|: z = 2 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ---------------------------------------- (41) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: a__zeros -{ 0 }-> 3 :|: a__zeros -{ 0 }-> 0 :|: a__zeros -{ 0 }-> 1 + 0 + 3 :|: ---------------------------------------- (42) Obligation: Complexity RNTS consisting of the following rules: A__AND(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 2, z0 >= 0, z' = z0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(a__length(mark(z0''))) + MARK(1 + z0'') :|: z = 1 + z0 + (1 + z0''), z0 >= 0, z0'' >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(a__and(mark(z0'), z1')) + MARK(1 + z0' + z1') :|: z = 1 + z0 + (1 + z0' + z1'), z0' >= 0, z1' >= 0, z0 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(3) + MARK(3) :|: z = 1 + z0 + 3, z0 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(2) + MARK(2) :|: z = 1 + z0 + 2, z0 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(1) + MARK(1) :|: z0 >= 0, z = 1 + z0 + 1 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(0) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(0) + MARK(3) :|: z = 1 + z0 + 3, z0 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(0) + MARK(0) :|: z0 >= 0, z = 1 + z0 + 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(1 + mark(z02)) + MARK(1 + z02) :|: z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(1 + mark(z01) + z1'') + MARK(1 + z01 + z1'') :|: z = 1 + z0 + (1 + z01 + z1''), z01 >= 0, z0 >= 0, z1'' >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(1 + 0 + 3) + MARK(3) :|: z = 1 + z0 + 3, z0 >= 0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(a__length(mark(z08))) + MARK(1 + z08) :|: z08 >= 0, z = 1 + (1 + z08) MARK(z) -{ 1 }-> 1 + A__LENGTH(a__and(mark(z07), z13)) + MARK(1 + z07 + z13) :|: z = 1 + (1 + z07 + z13), z07 >= 0, z13 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(3) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__LENGTH(2) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__LENGTH(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__LENGTH(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(0) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__LENGTH(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(1 + mark(z010)) + MARK(1 + z010) :|: z = 1 + (1 + z010), z010 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(1 + mark(z09) + z14) + MARK(1 + z09 + z14) :|: z = 1 + (1 + z09 + z14), z09 >= 0, z14 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(1 + 0 + 3) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__AND(a__length(mark(z04)), z1) + MARK(1 + z04) :|: z04 >= 0, z1 >= 0, z = 1 + (1 + z04) + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__and(mark(z03), z11), z1) + MARK(1 + z03 + z11) :|: z11 >= 0, z1 >= 0, z03 >= 0, z = 1 + (1 + z03 + z11) + z1 MARK(z) -{ 1 }-> 1 + A__AND(3, z1) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 MARK(z) -{ 1 }-> 1 + A__AND(2, z1) + MARK(2) :|: z1 >= 0, z = 1 + 2 + z1 MARK(z) -{ 1 }-> 1 + A__AND(1, z1) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 MARK(z) -{ 1 }-> 1 + A__AND(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__AND(0, z1) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 MARK(z) -{ 1 }-> 1 + A__AND(0, z1) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 MARK(z) -{ 1 }-> 1 + A__AND(1 + mark(z06), z1) + MARK(1 + z06) :|: z1 >= 0, z = 1 + (1 + z06) + z1, z06 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(1 + mark(z05) + z12, z1) + MARK(1 + z05 + z12) :|: z = 1 + (1 + z05 + z12) + z1, z1 >= 0, z12 >= 0, z05 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(1 + 0 + 3, z1) + MARK(3) :|: z1 >= 0, z = 1 + 3 + z1 a__and(z, z') -{ 0 }-> mark(z0) :|: z = 2, z0 >= 0, z' = z0 a__and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__and(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__length(z) -{ 0 }-> 0 :|: z = 1 a__length(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__length(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__length(z) -{ 0 }-> 1 + a__length(a__length(mark(z012))) :|: z = 1 + z0 + (1 + z012), z0 >= 0, z012 >= 0 a__length(z) -{ 0 }-> 1 + a__length(a__and(mark(z011), z15)) :|: z011 >= 0, z15 >= 0, z = 1 + z0 + (1 + z011 + z15), z0 >= 0 a__length(z) -{ 0 }-> 1 + a__length(3) :|: z = 1 + z0 + 3, z0 >= 0 a__length(z) -{ 0 }-> 1 + a__length(2) :|: z = 1 + z0 + 2, z0 >= 0 a__length(z) -{ 0 }-> 1 + a__length(1) :|: z0 >= 0, z = 1 + z0 + 1 a__length(z) -{ 0 }-> 1 + a__length(0) :|: z0 >= 0, z = 1 + z0 + 0 a__length(z) -{ 0 }-> 1 + a__length(0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__length(z) -{ 0 }-> 1 + a__length(0) :|: z = 1 + z0 + 3, z0 >= 0 a__length(z) -{ 0 }-> 1 + a__length(1 + mark(z014)) :|: z = 1 + z0 + (1 + z014), z014 >= 0, z0 >= 0 a__length(z) -{ 0 }-> 1 + a__length(1 + mark(z013) + z16) :|: z013 >= 0, z0 >= 0, z16 >= 0, z = 1 + z0 + (1 + z013 + z16) a__length(z) -{ 0 }-> 1 + a__length(1 + 0 + 3) :|: z = 1 + z0 + 3, z0 >= 0 a__zeros -{ 0 }-> 3 :|: a__zeros -{ 0 }-> 0 :|: a__zeros -{ 0 }-> 1 + 0 + 3 :|: mark(z) -{ 0 }-> a__length(a__length(mark(z020))) :|: z = 1 + (1 + z020), z020 >= 0 mark(z) -{ 0 }-> a__length(a__and(mark(z019), z19)) :|: z019 >= 0, z19 >= 0, z = 1 + (1 + z019 + z19) mark(z) -{ 0 }-> a__length(3) :|: z = 1 + 3 mark(z) -{ 0 }-> a__length(2) :|: z = 1 + 2 mark(z) -{ 0 }-> a__length(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__length(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__length(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__length(0) :|: z = 1 + 3 mark(z) -{ 0 }-> a__length(1 + mark(z022)) :|: z022 >= 0, z = 1 + (1 + z022) mark(z) -{ 0 }-> a__length(1 + mark(z021) + z110) :|: z021 >= 0, z110 >= 0, z = 1 + (1 + z021 + z110) mark(z) -{ 0 }-> a__length(1 + 0 + 3) :|: z = 1 + 3 mark(z) -{ 0 }-> a__and(a__length(mark(z016)), z1) :|: z1 >= 0, z016 >= 0, z = 1 + (1 + z016) + z1 mark(z) -{ 0 }-> a__and(a__and(mark(z015), z17), z1) :|: z015 >= 0, z1 >= 0, z = 1 + (1 + z015 + z17) + z1, z17 >= 0 mark(z) -{ 0 }-> a__and(3, z1) :|: z1 >= 0, z = 1 + 3 + z1 mark(z) -{ 0 }-> a__and(2, z1) :|: z1 >= 0, z = 1 + 2 + z1 mark(z) -{ 0 }-> a__and(1, z1) :|: z1 >= 0, z = 1 + 1 + z1 mark(z) -{ 0 }-> a__and(0, z1) :|: z1 >= 0, z = 1 + 0 + z1 mark(z) -{ 0 }-> a__and(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__and(0, z1) :|: z1 >= 0, z = 1 + 3 + z1 mark(z) -{ 0 }-> a__and(1 + mark(z018), z1) :|: z1 >= 0, z = 1 + (1 + z018) + z1, z018 >= 0 mark(z) -{ 0 }-> a__and(1 + mark(z017) + z18, z1) :|: z18 >= 0, z1 >= 0, z = 1 + (1 + z017 + z18) + z1, z017 >= 0 mark(z) -{ 0 }-> a__and(1 + 0 + 3, z1) :|: z1 >= 0, z = 1 + 3 + z1 mark(z) -{ 0 }-> 3 :|: z = 3 mark(z) -{ 0 }-> 2 :|: z = 2 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 0 :|: z = 3 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 1 + 0 + 3 :|: z = 3 ---------------------------------------- (43) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (44) Obligation: Complexity RNTS consisting of the following rules: A__AND(z, z') -{ 1 }-> 1 + MARK(z') :|: z = 2, z' >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(a__length(mark(z0''))) + MARK(1 + z0'') :|: z = 1 + z0 + (1 + z0''), z0 >= 0, z0'' >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(a__and(mark(z0'), z1')) + MARK(1 + z0' + z1') :|: z = 1 + z0 + (1 + z0' + z1'), z0' >= 0, z1' >= 0, z0 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(3) + MARK(3) :|: z - 4 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(2) + MARK(2) :|: z - 3 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(1) + MARK(1) :|: z - 2 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(0) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(0) + MARK(3) :|: z - 4 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(0) + MARK(0) :|: z - 1 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(1 + mark(z02)) + MARK(1 + z02) :|: z = 1 + z0 + (1 + z02), z02 >= 0, z0 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(1 + mark(z01) + z1'') + MARK(1 + z01 + z1'') :|: z = 1 + z0 + (1 + z01 + z1''), z01 >= 0, z0 >= 0, z1'' >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(1 + 0 + 3) + MARK(3) :|: z - 4 >= 0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(a__length(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(a__and(mark(z07), z13)) + MARK(1 + z07 + z13) :|: z = 1 + (1 + z07 + z13), z07 >= 0, z13 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(3) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__LENGTH(2) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__LENGTH(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__LENGTH(0) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__LENGTH(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(0) + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(1 + mark(z - 2)) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(1 + mark(z09) + z14) + MARK(1 + z09 + z14) :|: z = 1 + (1 + z09 + z14), z09 >= 0, z14 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(1 + 0 + 3) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__AND(a__length(mark(z04)), z1) + MARK(1 + z04) :|: z04 >= 0, z1 >= 0, z = 1 + (1 + z04) + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__and(mark(z03), z11), z1) + MARK(1 + z03 + z11) :|: z11 >= 0, z1 >= 0, z03 >= 0, z = 1 + (1 + z03 + z11) + z1 MARK(z) -{ 1 }-> 1 + A__AND(3, z - 4) + MARK(3) :|: z - 4 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(2, z - 3) + MARK(2) :|: z - 3 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(1, z - 2) + MARK(1) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__AND(0, z - 4) + MARK(3) :|: z - 4 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(0, z - 1) + MARK(0) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(1 + mark(z06), z1) + MARK(1 + z06) :|: z1 >= 0, z = 1 + (1 + z06) + z1, z06 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(1 + mark(z05) + z12, z1) + MARK(1 + z05 + z12) :|: z = 1 + (1 + z05 + z12) + z1, z1 >= 0, z12 >= 0, z05 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(1 + 0 + 3, z - 4) + MARK(3) :|: z - 4 >= 0 a__and(z, z') -{ 0 }-> mark(z') :|: z = 2, z' >= 0 a__and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__and(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__length(z) -{ 0 }-> 0 :|: z = 1 a__length(z) -{ 0 }-> 0 :|: z >= 0 a__length(z) -{ 0 }-> 1 + z :|: z >= 0 a__length(z) -{ 0 }-> 1 + a__length(a__length(mark(z012))) :|: z = 1 + z0 + (1 + z012), z0 >= 0, z012 >= 0 a__length(z) -{ 0 }-> 1 + a__length(a__and(mark(z011), z15)) :|: z011 >= 0, z15 >= 0, z = 1 + z0 + (1 + z011 + z15), z0 >= 0 a__length(z) -{ 0 }-> 1 + a__length(3) :|: z - 4 >= 0 a__length(z) -{ 0 }-> 1 + a__length(2) :|: z - 3 >= 0 a__length(z) -{ 0 }-> 1 + a__length(1) :|: z - 2 >= 0 a__length(z) -{ 0 }-> 1 + a__length(0) :|: z - 1 >= 0 a__length(z) -{ 0 }-> 1 + a__length(0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__length(z) -{ 0 }-> 1 + a__length(0) :|: z - 4 >= 0 a__length(z) -{ 0 }-> 1 + a__length(1 + mark(z014)) :|: z = 1 + z0 + (1 + z014), z014 >= 0, z0 >= 0 a__length(z) -{ 0 }-> 1 + a__length(1 + mark(z013) + z16) :|: z013 >= 0, z0 >= 0, z16 >= 0, z = 1 + z0 + (1 + z013 + z16) a__length(z) -{ 0 }-> 1 + a__length(1 + 0 + 3) :|: z - 4 >= 0 a__zeros -{ 0 }-> 3 :|: a__zeros -{ 0 }-> 0 :|: a__zeros -{ 0 }-> 1 + 0 + 3 :|: mark(z) -{ 0 }-> a__length(a__length(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__length(a__and(mark(z019), z19)) :|: z019 >= 0, z19 >= 0, z = 1 + (1 + z019 + z19) mark(z) -{ 0 }-> a__length(3) :|: z = 1 + 3 mark(z) -{ 0 }-> a__length(2) :|: z = 1 + 2 mark(z) -{ 0 }-> a__length(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__length(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__length(0) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__length(0) :|: z = 1 + 3 mark(z) -{ 0 }-> a__length(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__length(1 + mark(z021) + z110) :|: z021 >= 0, z110 >= 0, z = 1 + (1 + z021 + z110) mark(z) -{ 0 }-> a__length(1 + 0 + 3) :|: z = 1 + 3 mark(z) -{ 0 }-> a__and(a__length(mark(z016)), z1) :|: z1 >= 0, z016 >= 0, z = 1 + (1 + z016) + z1 mark(z) -{ 0 }-> a__and(a__and(mark(z015), z17), z1) :|: z015 >= 0, z1 >= 0, z = 1 + (1 + z015 + z17) + z1, z17 >= 0 mark(z) -{ 0 }-> a__and(3, z - 4) :|: z - 4 >= 0 mark(z) -{ 0 }-> a__and(2, z - 3) :|: z - 3 >= 0 mark(z) -{ 0 }-> a__and(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__and(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__and(0, z - 4) :|: z - 4 >= 0 mark(z) -{ 0 }-> a__and(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__and(1 + mark(z018), z1) :|: z1 >= 0, z = 1 + (1 + z018) + z1, z018 >= 0 mark(z) -{ 0 }-> a__and(1 + mark(z017) + z18, z1) :|: z18 >= 0, z1 >= 0, z = 1 + (1 + z017 + z18) + z1, z017 >= 0 mark(z) -{ 0 }-> a__and(1 + 0 + 3, z - 4) :|: z - 4 >= 0 mark(z) -{ 0 }-> 3 :|: z = 3 mark(z) -{ 0 }-> 2 :|: z = 2 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: z >= 0 mark(z) -{ 0 }-> 0 :|: z = 3 mark(z) -{ 0 }-> 1 + mark(z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 1 + 0 + 3 :|: z = 3 ---------------------------------------- (45) 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__zeros -> null_a__zeros [0] a__and(v0, v1) -> null_a__and [0] a__length(v0) -> null_a__length [0] mark(v0) -> null_mark [0] A__AND(v0, v1) -> null_A__AND [0] A__LENGTH(v0) -> null_A__LENGTH [0] MARK(v0) -> null_MARK [0] And the following fresh constants: null_a__zeros, null_a__and, null_a__length, null_mark, null_A__AND, null_A__LENGTH, null_MARK ---------------------------------------- (46) 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__AND(tt, z0) -> c2(MARK(z0)) [1] A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) [1] MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) [1] MARK(cons(z0, z1)) -> c10(MARK(z0)) [1] MARK(s(z0)) -> c14(MARK(z0)) [1] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__and(tt, z0) -> mark(z0) [0] a__and(z0, z1) -> and(z0, z1) [0] a__length(nil) -> 0 [0] a__length(cons(z0, z1)) -> s(a__length(mark(z1))) [0] a__length(z0) -> length(z0) [0] mark(zeros) -> a__zeros [0] mark(and(z0, z1)) -> a__and(mark(z0), z1) [0] mark(length(z0)) -> a__length(mark(z0)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(tt) -> tt [0] mark(nil) -> nil [0] mark(s(z0)) -> s(mark(z0)) [0] a__zeros -> null_a__zeros [0] a__and(v0, v1) -> null_a__and [0] a__length(v0) -> null_a__length [0] mark(v0) -> null_mark [0] A__AND(v0, v1) -> null_A__AND [0] A__LENGTH(v0) -> null_A__LENGTH [0] MARK(v0) -> null_MARK [0] The TRS has the following type information: A__AND :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> c2:null_A__AND tt :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark c2 :: c8:c9:c10:c14:null_MARK -> c2:null_A__AND MARK :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> c8:c9:c10:c14:null_MARK A__LENGTH :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> c5:null_A__LENGTH cons :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark c5 :: c5:null_A__LENGTH -> c8:c9:c10:c14:null_MARK -> c5:null_A__LENGTH mark :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark and :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark c8 :: c2:null_A__AND -> c8:c9:c10:c14:null_MARK -> c8:c9:c10:c14:null_MARK length :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark c9 :: c5:null_A__LENGTH -> c8:c9:c10:c14:null_MARK -> c8:c9:c10:c14:null_MARK c10 :: c8:c9:c10:c14:null_MARK -> c8:c9:c10:c14:null_MARK s :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark c14 :: c8:c9:c10:c14:null_MARK -> c8:c9:c10:c14:null_MARK a__zeros :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark 0 :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark zeros :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark a__and :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark a__length :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark -> tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark nil :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark null_a__zeros :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark null_a__and :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark null_a__length :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark null_mark :: tt:cons:and:length:s:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_mark null_A__AND :: c2:null_A__AND null_A__LENGTH :: c5:null_A__LENGTH null_MARK :: c8:c9:c10:c14:null_MARK Rewrite Strategy: INNERMOST ---------------------------------------- (47) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 2 0 => 0 zeros => 3 nil => 1 null_a__zeros => 0 null_a__and => 0 null_a__length => 0 null_mark => 0 null_A__AND => 0 null_A__LENGTH => 0 null_MARK => 0 ---------------------------------------- (48) Obligation: Complexity RNTS consisting of the following rules: A__AND(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__AND(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 2, z0 >= 0, z' = z0 A__LENGTH(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__and(z, z') -{ 0 }-> mark(z0) :|: z = 2, z0 >= 0, z' = z0 a__and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__and(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__length(z) -{ 0 }-> 0 :|: z = 1 a__length(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__length(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__length(z) -{ 0 }-> 1 + a__length(mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__zeros -{ 0 }-> 3 :|: a__zeros -{ 0 }-> 0 :|: a__zeros -{ 0 }-> 1 + 0 + 3 :|: mark(z) -{ 0 }-> a__zeros :|: z = 3 mark(z) -{ 0 }-> a__length(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__and(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 2 :|: z = 2 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (49) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) by A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros), MARK(zeros)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, 0)) -> c5(A__LENGTH(0), MARK(0)) A__LENGTH(cons(x0, tt)) -> c5(A__LENGTH(tt), MARK(tt)) A__LENGTH(cons(x0, nil)) -> c5(A__LENGTH(nil), MARK(nil)) A__LENGTH(cons(x0, s(z0))) -> c5(A__LENGTH(s(mark(z0))), MARK(s(z0))) ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros), MARK(zeros)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, 0)) -> c5(A__LENGTH(0), MARK(0)) A__LENGTH(cons(x0, tt)) -> c5(A__LENGTH(tt), MARK(tt)) A__LENGTH(cons(x0, nil)) -> c5(A__LENGTH(nil), MARK(nil)) A__LENGTH(cons(x0, s(z0))) -> c5(A__LENGTH(s(mark(z0))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros), MARK(zeros)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, 0)) -> c5(A__LENGTH(0), MARK(0)) A__LENGTH(cons(x0, tt)) -> c5(A__LENGTH(tt), MARK(tt)) A__LENGTH(cons(x0, nil)) -> c5(A__LENGTH(nil), MARK(nil)) A__LENGTH(cons(x0, s(z0))) -> c5(A__LENGTH(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_2, c9_2, c10_1, c14_1, c5_2 ---------------------------------------- (51) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: A__LENGTH(cons(x0, 0)) -> c5(A__LENGTH(0), MARK(0)) A__LENGTH(cons(x0, tt)) -> c5(A__LENGTH(tt), MARK(tt)) A__LENGTH(cons(x0, nil)) -> c5(A__LENGTH(nil), MARK(nil)) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros), MARK(zeros)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(A__LENGTH(s(mark(z0))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros), MARK(zeros)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(A__LENGTH(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_2, c9_2, c10_1, c14_1, c5_2 ---------------------------------------- (53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_2, c9_2, c10_1, c14_1, c5_2, c5_1 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(z0, z1)) -> c8(A__AND(mark(z0), z1), MARK(z0)) by MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(cons(z0, z1), x1)) -> c8(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(0, x1)) -> c8(A__AND(0, x1), MARK(0)) MARK(and(tt, x1)) -> c8(A__AND(tt, x1), MARK(tt)) MARK(and(nil, x1)) -> c8(A__AND(nil, x1), MARK(nil)) MARK(and(s(z0), x1)) -> c8(A__AND(s(mark(z0)), x1), MARK(s(z0))) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(cons(z0, z1), x1)) -> c8(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(0, x1)) -> c8(A__AND(0, x1), MARK(0)) MARK(and(tt, x1)) -> c8(A__AND(tt, x1), MARK(tt)) MARK(and(nil, x1)) -> c8(A__AND(nil, x1), MARK(nil)) MARK(and(s(z0), x1)) -> c8(A__AND(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(cons(z0, z1), x1)) -> c8(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(0, x1)) -> c8(A__AND(0, x1), MARK(0)) MARK(and(tt, x1)) -> c8(A__AND(tt, x1), MARK(tt)) MARK(and(nil, x1)) -> c8(A__AND(nil, x1), MARK(nil)) MARK(and(s(z0), x1)) -> c8(A__AND(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c9_2, c10_1, c14_1, c5_2, c5_1, c8_2 ---------------------------------------- (57) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(and(nil, x1)) -> c8(A__AND(nil, x1), MARK(nil)) MARK(and(0, x1)) -> c8(A__AND(0, x1), MARK(0)) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(cons(z0, z1), x1)) -> c8(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c8(A__AND(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(cons(z0, z1), x1)) -> c8(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c8(A__AND(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c9_2, c10_1, c14_1, c5_2, c5_1, c8_2 ---------------------------------------- (59) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c9_2, c10_1, c14_1, c5_2, c5_1, c8_2, c8_1 ---------------------------------------- (61) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(z0)) -> c9(A__LENGTH(mark(z0)), MARK(z0)) by MARK(length(zeros)) -> c9(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(0)) -> c9(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c9(A__LENGTH(tt), MARK(tt)) MARK(length(nil)) -> c9(A__LENGTH(nil), MARK(nil)) MARK(length(s(z0))) -> c9(A__LENGTH(s(mark(z0))), MARK(s(z0))) ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(0)) -> c9(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c9(A__LENGTH(tt), MARK(tt)) MARK(length(nil)) -> c9(A__LENGTH(nil), MARK(nil)) MARK(length(s(z0))) -> c9(A__LENGTH(s(mark(z0))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(0)) -> c9(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c9(A__LENGTH(tt), MARK(tt)) MARK(length(nil)) -> c9(A__LENGTH(nil), MARK(nil)) MARK(length(s(z0))) -> c9(A__LENGTH(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_2, c8_1, c9_2 ---------------------------------------- (63) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(length(tt)) -> c9(A__LENGTH(tt), MARK(tt)) MARK(length(nil)) -> c9(A__LENGTH(nil), MARK(nil)) MARK(length(0)) -> c9(A__LENGTH(0), MARK(0)) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(A__LENGTH(s(mark(z0))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(A__LENGTH(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_2, c8_1, c9_2 ---------------------------------------- (65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_2, c8_1, c9_2, c9_1 ---------------------------------------- (67) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) by A__LENGTH(cons(x0, and(x1, z1))) -> c5(A__LENGTH(and(mark(x1), z1)), MARK(and(x1, z1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2)), MARK(and(0, x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2)), MARK(and(nil, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(A__LENGTH(and(mark(x1), z1)), MARK(and(x1, z1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2)), MARK(and(0, x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2)), MARK(and(nil, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(A__LENGTH(and(mark(x1), z1)), MARK(and(x1, z1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2)), MARK(and(0, x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2)), MARK(and(nil, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_2, c8_1, c9_2, c9_1 ---------------------------------------- (69) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_2, c8_1, c9_2, c9_1 ---------------------------------------- (71) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) by A__LENGTH(cons(x0, length(x1))) -> c5(A__LENGTH(length(mark(x1))), MARK(length(x1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0)), MARK(length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt)), MARK(length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil)), MARK(length(nil))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(x1))) -> c5(A__LENGTH(length(mark(x1))), MARK(length(x1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0)), MARK(length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt)), MARK(length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil)), MARK(length(nil))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(x1))) -> c5(A__LENGTH(length(mark(x1))), MARK(length(x1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0)), MARK(length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt)), MARK(length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil)), MARK(length(nil))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_2, c8_1, c9_2, c9_1 ---------------------------------------- (73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_2, c8_1, c9_2, c9_1 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) by A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(zeros)) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(zeros)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(zeros)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_2, c8_1, c9_2, c9_1 ---------------------------------------- (77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(zeros)) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_2, c8_1, c9_2, c9_1 ---------------------------------------- (79) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(and(z0, z1), x1)) -> c8(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) by MARK(and(and(x0, z1), x2)) -> c8(A__AND(and(mark(x0), z1), x2), MARK(and(x0, z1))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2), MARK(and(0, x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2), MARK(and(nil, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(x0, z1), x2)) -> c8(A__AND(and(mark(x0), z1), x2), MARK(and(x0, z1))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2), MARK(and(0, x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2), MARK(and(nil, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(x0, z1), x2)) -> c8(A__AND(and(mark(x0), z1), x2), MARK(and(x0, z1))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2), MARK(and(0, x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2), MARK(and(nil, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_2, c8_1, c9_2, c9_1 ---------------------------------------- (81) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_2, c8_1, c9_2, c9_1 ---------------------------------------- (83) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(length(z0), x1)) -> c8(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) by MARK(and(length(x0), x1)) -> c8(A__AND(length(mark(x0)), x1), MARK(length(x0))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1), MARK(length(0))) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1), MARK(length(tt))) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1), MARK(length(nil))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(x0), x1)) -> c8(A__AND(length(mark(x0)), x1), MARK(length(x0))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1), MARK(length(0))) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1), MARK(length(tt))) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1), MARK(length(nil))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(x0), x1)) -> c8(A__AND(length(mark(x0)), x1), MARK(length(x0))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1), MARK(length(0))) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1), MARK(length(tt))) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1), MARK(length(nil))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (85) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (87) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(zeros, x1)) -> c8(A__AND(a__zeros, x1)) by MARK(and(zeros, x0)) -> c8(A__AND(cons(0, zeros), x0)) MARK(and(zeros, x0)) -> c8(A__AND(zeros, x0)) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) MARK(and(zeros, x0)) -> c8(A__AND(cons(0, zeros), x0)) MARK(and(zeros, x0)) -> c8(A__AND(zeros, x0)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) MARK(and(zeros, x0)) -> c8(A__AND(cons(0, zeros), x0)) MARK(and(zeros, x0)) -> c8(A__AND(zeros, x0)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (89) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(and(zeros, x0)) -> c8(A__AND(zeros, x0)) MARK(and(zeros, x0)) -> c8(A__AND(cons(0, zeros), x0)) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(and(z0, z1))) -> c9(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) by MARK(length(and(x0, z1))) -> c9(A__LENGTH(and(mark(x0), z1)), MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1)), MARK(and(zeros, x1))) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1)), MARK(and(0, x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1)), MARK(and(nil, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(x0, z1))) -> c9(A__LENGTH(and(mark(x0), z1)), MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1)), MARK(and(zeros, x1))) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1)), MARK(and(0, x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1)), MARK(and(nil, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(x0, z1))) -> c9(A__LENGTH(and(mark(x0), z1)), MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1)), MARK(and(zeros, x1))) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1)), MARK(and(0, x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1)), MARK(and(nil, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(length(z0))) -> c9(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) by MARK(length(length(x0))) -> c9(A__LENGTH(length(mark(x0))), MARK(length(x0))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0)), MARK(length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt)), MARK(length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil)), MARK(length(nil))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(x0))) -> c9(A__LENGTH(length(mark(x0))), MARK(length(x0))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0)), MARK(length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt)), MARK(length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil)), MARK(length(nil))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(x0))) -> c9(A__LENGTH(length(mark(x0))), MARK(length(x0))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0)), MARK(length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt)), MARK(length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil)), MARK(length(nil))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (99) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(zeros)) -> c9(A__LENGTH(a__zeros)) by MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) MARK(length(zeros)) -> c9(A__LENGTH(zeros)) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) MARK(length(zeros)) -> c9(A__LENGTH(zeros)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) MARK(length(zeros)) -> c9(A__LENGTH(zeros)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (103) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(length(zeros)) -> c9(A__LENGTH(zeros)) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) by A__LENGTH(cons(x0, and(0, z1))) -> c5(A__LENGTH(and(0, z1))) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__LENGTH(cons(x0, and(0, z1))) -> c5(A__LENGTH(and(0, z1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__LENGTH(cons(x0, and(0, z1))) -> c5(A__LENGTH(and(0, z1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__LENGTH(cons(x0, and(0, z1))) -> c5(A__LENGTH(and(0, z1))) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) by A__LENGTH(cons(x0, and(nil, z1))) -> c5(A__LENGTH(and(nil, z1))) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__LENGTH(cons(x0, and(nil, z1))) -> c5(A__LENGTH(and(nil, z1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__LENGTH(cons(x0, and(nil, z1))) -> c5(A__LENGTH(and(nil, z1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (111) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__LENGTH(cons(x0, and(nil, z1))) -> c5(A__LENGTH(and(nil, z1))) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) by A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(length(0))) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(length(0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(length(0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (115) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(length(0))) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) by A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(length(tt))) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(length(tt))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(length(tt))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (119) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(length(tt))) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (121) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) by A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(0)) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(length(nil))) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(0)) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(length(nil))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(0)) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(length(nil))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (123) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(0)) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(length(nil))) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (125) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(and(0, x1), x2)) -> c8(A__AND(a__and(0, x1), x2)) by MARK(and(and(0, z1), x1)) -> c8(A__AND(and(0, z1), x1)) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) MARK(and(and(0, z1), x1)) -> c8(A__AND(and(0, z1), x1)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) MARK(and(and(0, z1), x1)) -> c8(A__AND(and(0, z1), x1)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (127) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(and(and(0, z1), x1)) -> c8(A__AND(and(0, z1), x1)) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (129) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(and(nil, x1), x2)) -> c8(A__AND(a__and(nil, x1), x2)) by MARK(and(and(nil, z1), x1)) -> c8(A__AND(and(nil, z1), x1)) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) MARK(and(and(nil, z1), x1)) -> c8(A__AND(and(nil, z1), x1)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) MARK(and(and(nil, z1), x1)) -> c8(A__AND(and(nil, z1), x1)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (131) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(and(and(nil, z1), x1)) -> c8(A__AND(and(nil, z1), x1)) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (133) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(length(0), x1)) -> c8(A__AND(a__length(0), x1)) by MARK(and(length(0), x0)) -> c8(A__AND(length(0), x0)) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) MARK(and(length(0), x0)) -> c8(A__AND(length(0), x0)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) MARK(and(length(0), x0)) -> c8(A__AND(length(0), x0)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (135) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(and(length(0), x0)) -> c8(A__AND(length(0), x0)) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (137) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(length(tt), x1)) -> c8(A__AND(a__length(tt), x1)) by MARK(and(length(tt), x0)) -> c8(A__AND(length(tt), x0)) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) MARK(and(length(tt), x0)) -> c8(A__AND(length(tt), x0)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) MARK(and(length(tt), x0)) -> c8(A__AND(length(tt), x0)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (139) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(and(length(tt), x0)) -> c8(A__AND(length(tt), x0)) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (141) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(length(nil), x1)) -> c8(A__AND(a__length(nil), x1)) by MARK(and(length(nil), x0)) -> c8(A__AND(0, x0)) MARK(and(length(nil), x0)) -> c8(A__AND(length(nil), x0)) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) MARK(and(length(nil), x0)) -> c8(A__AND(0, x0)) MARK(and(length(nil), x0)) -> c8(A__AND(length(nil), x0)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) MARK(and(length(nil), x0)) -> c8(A__AND(0, x0)) MARK(and(length(nil), x0)) -> c8(A__AND(length(nil), x0)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (143) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(and(length(nil), x0)) -> c8(A__AND(length(nil), x0)) MARK(and(length(nil), x0)) -> c8(A__AND(0, x0)) ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (145) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(and(0, x1))) -> c9(A__LENGTH(a__and(0, x1))) by MARK(length(and(0, z1))) -> c9(A__LENGTH(and(0, z1))) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) MARK(length(and(0, z1))) -> c9(A__LENGTH(and(0, z1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) MARK(length(and(0, z1))) -> c9(A__LENGTH(and(0, z1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (147) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(length(and(0, z1))) -> c9(A__LENGTH(and(0, z1))) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (149) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(and(nil, x1))) -> c9(A__LENGTH(a__and(nil, x1))) by MARK(length(and(nil, z1))) -> c9(A__LENGTH(and(nil, z1))) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) MARK(length(and(nil, z1))) -> c9(A__LENGTH(and(nil, z1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) MARK(length(and(nil, z1))) -> c9(A__LENGTH(and(nil, z1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (151) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(length(and(nil, z1))) -> c9(A__LENGTH(and(nil, z1))) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (153) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(length(0))) -> c9(A__LENGTH(a__length(0))) by MARK(length(length(0))) -> c9(A__LENGTH(length(0))) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) MARK(length(length(0))) -> c9(A__LENGTH(length(0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) MARK(length(length(0))) -> c9(A__LENGTH(length(0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (155) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(length(length(0))) -> c9(A__LENGTH(length(0))) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (157) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(length(tt))) -> c9(A__LENGTH(a__length(tt))) by MARK(length(length(tt))) -> c9(A__LENGTH(length(tt))) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) MARK(length(length(tt))) -> c9(A__LENGTH(length(tt))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) MARK(length(length(tt))) -> c9(A__LENGTH(length(tt))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (159) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(length(length(tt))) -> c9(A__LENGTH(length(tt))) ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (161) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(length(nil))) -> c9(A__LENGTH(a__length(nil))) by MARK(length(length(nil))) -> c9(A__LENGTH(0)) MARK(length(length(nil))) -> c9(A__LENGTH(length(nil))) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) MARK(length(length(nil))) -> c9(A__LENGTH(0)) MARK(length(length(nil))) -> c9(A__LENGTH(length(nil))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) MARK(length(length(nil))) -> c9(A__LENGTH(0)) MARK(length(length(nil))) -> c9(A__LENGTH(length(nil))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (163) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(length(length(nil))) -> c9(A__LENGTH(length(nil))) MARK(length(length(nil))) -> c9(A__LENGTH(0)) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__AND_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2 ---------------------------------------- (165) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace A__AND(tt, z0) -> c2(MARK(z0)) by A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) S tuples: MARK(cons(z0, z1)) -> c10(MARK(z0)) MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: MARK_1, A__LENGTH_1, A__AND_2 Compound Symbols: c10_1, c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2, c2_1 ---------------------------------------- (167) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(cons(z0, z1)) -> c10(MARK(z0)) by MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) MARK(cons(and(and(cons(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(cons(y0, y1), y2), y3))) MARK(cons(and(and(tt, y0), y1), z1)) -> c10(MARK(and(and(tt, y0), y1))) MARK(cons(and(and(s(y0), y1), y2), z1)) -> c10(MARK(and(and(s(y0), y1), y2))) MARK(cons(and(and(y0, y1), y2), z1)) -> c10(MARK(and(and(y0, y1), y2))) MARK(cons(and(length(zeros), y0), z1)) -> c10(MARK(and(length(zeros), y0))) MARK(cons(and(length(and(y0, y1)), y2), z1)) -> c10(MARK(and(length(and(y0, y1)), y2))) MARK(cons(and(length(length(y0)), y1), z1)) -> c10(MARK(and(length(length(y0)), y1))) MARK(cons(and(length(cons(y0, y1)), y2), z1)) -> c10(MARK(and(length(cons(y0, y1)), y2))) MARK(cons(and(length(s(y0)), y1), z1)) -> c10(MARK(and(length(s(y0)), y1))) MARK(cons(and(length(y0), y1), z1)) -> c10(MARK(and(length(y0), y1))) MARK(cons(and(and(zeros, y0), y1), z1)) -> c10(MARK(and(and(zeros, y0), y1))) MARK(cons(length(and(and(y0, y1), y2)), z1)) -> c10(MARK(length(and(and(y0, y1), y2)))) MARK(cons(length(and(length(y0), y1)), z1)) -> c10(MARK(length(and(length(y0), y1)))) MARK(cons(length(and(cons(y0, y1), y2)), z1)) -> c10(MARK(length(and(cons(y0, y1), y2)))) MARK(cons(length(and(tt, y0)), z1)) -> c10(MARK(length(and(tt, y0)))) MARK(cons(length(and(s(y0), y1)), z1)) -> c10(MARK(length(and(s(y0), y1)))) MARK(cons(length(and(y0, y1)), z1)) -> c10(MARK(length(and(y0, y1)))) MARK(cons(length(and(zeros, y0)), z1)) -> c10(MARK(length(and(zeros, y0)))) MARK(cons(length(length(zeros)), z1)) -> c10(MARK(length(length(zeros)))) MARK(cons(length(length(and(y0, y1))), z1)) -> c10(MARK(length(length(and(y0, y1))))) MARK(cons(length(length(length(y0))), z1)) -> c10(MARK(length(length(length(y0))))) MARK(cons(length(length(cons(y0, y1))), z1)) -> c10(MARK(length(length(cons(y0, y1))))) MARK(cons(length(length(s(y0))), z1)) -> c10(MARK(length(length(s(y0))))) MARK(cons(length(length(y0)), z1)) -> c10(MARK(length(length(y0)))) MARK(cons(length(zeros), z1)) -> c10(MARK(length(zeros))) ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) MARK(cons(and(and(cons(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(cons(y0, y1), y2), y3))) MARK(cons(and(and(tt, y0), y1), z1)) -> c10(MARK(and(and(tt, y0), y1))) MARK(cons(and(and(s(y0), y1), y2), z1)) -> c10(MARK(and(and(s(y0), y1), y2))) MARK(cons(and(and(y0, y1), y2), z1)) -> c10(MARK(and(and(y0, y1), y2))) MARK(cons(and(length(zeros), y0), z1)) -> c10(MARK(and(length(zeros), y0))) MARK(cons(and(length(and(y0, y1)), y2), z1)) -> c10(MARK(and(length(and(y0, y1)), y2))) MARK(cons(and(length(length(y0)), y1), z1)) -> c10(MARK(and(length(length(y0)), y1))) MARK(cons(and(length(cons(y0, y1)), y2), z1)) -> c10(MARK(and(length(cons(y0, y1)), y2))) MARK(cons(and(length(s(y0)), y1), z1)) -> c10(MARK(and(length(s(y0)), y1))) MARK(cons(and(length(y0), y1), z1)) -> c10(MARK(and(length(y0), y1))) MARK(cons(and(and(zeros, y0), y1), z1)) -> c10(MARK(and(and(zeros, y0), y1))) MARK(cons(length(and(and(y0, y1), y2)), z1)) -> c10(MARK(length(and(and(y0, y1), y2)))) MARK(cons(length(and(length(y0), y1)), z1)) -> c10(MARK(length(and(length(y0), y1)))) MARK(cons(length(and(cons(y0, y1), y2)), z1)) -> c10(MARK(length(and(cons(y0, y1), y2)))) MARK(cons(length(and(tt, y0)), z1)) -> c10(MARK(length(and(tt, y0)))) MARK(cons(length(and(s(y0), y1)), z1)) -> c10(MARK(length(and(s(y0), y1)))) MARK(cons(length(and(y0, y1)), z1)) -> c10(MARK(length(and(y0, y1)))) MARK(cons(length(and(zeros, y0)), z1)) -> c10(MARK(length(and(zeros, y0)))) MARK(cons(length(length(zeros)), z1)) -> c10(MARK(length(length(zeros)))) MARK(cons(length(length(and(y0, y1))), z1)) -> c10(MARK(length(length(and(y0, y1))))) MARK(cons(length(length(length(y0))), z1)) -> c10(MARK(length(length(length(y0))))) MARK(cons(length(length(cons(y0, y1))), z1)) -> c10(MARK(length(length(cons(y0, y1))))) MARK(cons(length(length(s(y0))), z1)) -> c10(MARK(length(length(s(y0))))) MARK(cons(length(length(y0)), z1)) -> c10(MARK(length(length(y0)))) MARK(cons(length(zeros), z1)) -> c10(MARK(length(zeros))) S tuples: MARK(s(z0)) -> c14(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) MARK(cons(and(and(cons(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(cons(y0, y1), y2), y3))) MARK(cons(and(and(tt, y0), y1), z1)) -> c10(MARK(and(and(tt, y0), y1))) MARK(cons(and(and(s(y0), y1), y2), z1)) -> c10(MARK(and(and(s(y0), y1), y2))) MARK(cons(and(and(y0, y1), y2), z1)) -> c10(MARK(and(and(y0, y1), y2))) MARK(cons(and(length(zeros), y0), z1)) -> c10(MARK(and(length(zeros), y0))) MARK(cons(and(length(and(y0, y1)), y2), z1)) -> c10(MARK(and(length(and(y0, y1)), y2))) MARK(cons(and(length(length(y0)), y1), z1)) -> c10(MARK(and(length(length(y0)), y1))) MARK(cons(and(length(cons(y0, y1)), y2), z1)) -> c10(MARK(and(length(cons(y0, y1)), y2))) MARK(cons(and(length(s(y0)), y1), z1)) -> c10(MARK(and(length(s(y0)), y1))) MARK(cons(and(length(y0), y1), z1)) -> c10(MARK(and(length(y0), y1))) MARK(cons(and(and(zeros, y0), y1), z1)) -> c10(MARK(and(and(zeros, y0), y1))) MARK(cons(length(and(and(y0, y1), y2)), z1)) -> c10(MARK(length(and(and(y0, y1), y2)))) MARK(cons(length(and(length(y0), y1)), z1)) -> c10(MARK(length(and(length(y0), y1)))) MARK(cons(length(and(cons(y0, y1), y2)), z1)) -> c10(MARK(length(and(cons(y0, y1), y2)))) MARK(cons(length(and(tt, y0)), z1)) -> c10(MARK(length(and(tt, y0)))) MARK(cons(length(and(s(y0), y1)), z1)) -> c10(MARK(length(and(s(y0), y1)))) MARK(cons(length(and(y0, y1)), z1)) -> c10(MARK(length(and(y0, y1)))) MARK(cons(length(and(zeros, y0)), z1)) -> c10(MARK(length(and(zeros, y0)))) MARK(cons(length(length(zeros)), z1)) -> c10(MARK(length(length(zeros)))) MARK(cons(length(length(and(y0, y1))), z1)) -> c10(MARK(length(length(and(y0, y1))))) MARK(cons(length(length(length(y0))), z1)) -> c10(MARK(length(length(length(y0))))) MARK(cons(length(length(cons(y0, y1))), z1)) -> c10(MARK(length(length(cons(y0, y1))))) MARK(cons(length(length(s(y0))), z1)) -> c10(MARK(length(length(s(y0))))) MARK(cons(length(length(y0)), z1)) -> c10(MARK(length(length(y0)))) MARK(cons(length(zeros), z1)) -> c10(MARK(length(zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: MARK_1, A__LENGTH_1, A__AND_2 Compound Symbols: c14_1, c5_2, c5_1, c8_1, c9_2, c9_1, c8_2, c2_1, c10_1 ---------------------------------------- (169) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(s(z0)) -> c14(MARK(z0)) by MARK(s(s(y0))) -> c14(MARK(s(y0))) MARK(s(and(cons(y0, y1), y2))) -> c14(MARK(and(cons(y0, y1), y2))) MARK(s(and(tt, y0))) -> c14(MARK(and(tt, y0))) MARK(s(and(s(y0), y1))) -> c14(MARK(and(s(y0), y1))) MARK(s(length(cons(y0, y1)))) -> c14(MARK(length(cons(y0, y1)))) MARK(s(length(s(y0)))) -> c14(MARK(length(s(y0)))) MARK(s(and(and(and(y0, y1), y2), y3))) -> c14(MARK(and(and(and(y0, y1), y2), y3))) MARK(s(and(and(length(y0), y1), y2))) -> c14(MARK(and(and(length(y0), y1), y2))) MARK(s(and(and(cons(y0, y1), y2), y3))) -> c14(MARK(and(and(cons(y0, y1), y2), y3))) MARK(s(and(and(tt, y0), y1))) -> c14(MARK(and(and(tt, y0), y1))) MARK(s(and(and(s(y0), y1), y2))) -> c14(MARK(and(and(s(y0), y1), y2))) MARK(s(and(and(y0, y1), y2))) -> c14(MARK(and(and(y0, y1), y2))) MARK(s(and(length(zeros), y0))) -> c14(MARK(and(length(zeros), y0))) MARK(s(and(length(and(y0, y1)), y2))) -> c14(MARK(and(length(and(y0, y1)), y2))) MARK(s(and(length(length(y0)), y1))) -> c14(MARK(and(length(length(y0)), y1))) MARK(s(and(length(cons(y0, y1)), y2))) -> c14(MARK(and(length(cons(y0, y1)), y2))) MARK(s(and(length(s(y0)), y1))) -> c14(MARK(and(length(s(y0)), y1))) MARK(s(and(length(y0), y1))) -> c14(MARK(and(length(y0), y1))) MARK(s(and(and(zeros, y0), y1))) -> c14(MARK(and(and(zeros, y0), y1))) MARK(s(length(and(and(y0, y1), y2)))) -> c14(MARK(length(and(and(y0, y1), y2)))) MARK(s(length(and(length(y0), y1)))) -> c14(MARK(length(and(length(y0), y1)))) MARK(s(length(and(cons(y0, y1), y2)))) -> c14(MARK(length(and(cons(y0, y1), y2)))) MARK(s(length(and(tt, y0)))) -> c14(MARK(length(and(tt, y0)))) MARK(s(length(and(s(y0), y1)))) -> c14(MARK(length(and(s(y0), y1)))) MARK(s(length(and(y0, y1)))) -> c14(MARK(length(and(y0, y1)))) MARK(s(length(and(zeros, y0)))) -> c14(MARK(length(and(zeros, y0)))) MARK(s(length(length(zeros)))) -> c14(MARK(length(length(zeros)))) MARK(s(length(length(and(y0, y1))))) -> c14(MARK(length(length(and(y0, y1))))) MARK(s(length(length(length(y0))))) -> c14(MARK(length(length(length(y0))))) MARK(s(length(length(cons(y0, y1))))) -> c14(MARK(length(length(cons(y0, y1))))) MARK(s(length(length(s(y0))))) -> c14(MARK(length(length(s(y0))))) MARK(s(length(length(y0)))) -> c14(MARK(length(length(y0)))) MARK(s(length(zeros))) -> c14(MARK(length(zeros))) MARK(s(cons(cons(y0, y1), y2))) -> c14(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c14(MARK(cons(s(y0), y1))) MARK(s(cons(and(cons(y0, y1), y2), y3))) -> c14(MARK(cons(and(cons(y0, y1), y2), y3))) MARK(s(cons(and(tt, y0), y1))) -> c14(MARK(cons(and(tt, y0), y1))) MARK(s(cons(and(s(y0), y1), y2))) -> c14(MARK(cons(and(s(y0), y1), y2))) MARK(s(cons(length(cons(y0, y1)), y2))) -> c14(MARK(cons(length(cons(y0, y1)), y2))) MARK(s(cons(length(s(y0)), y1))) -> c14(MARK(cons(length(s(y0)), y1))) MARK(s(cons(and(and(and(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(and(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(length(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(length(y0), y1), y2), y3))) MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(cons(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(tt, y0), y1), y2))) -> c14(MARK(cons(and(and(tt, y0), y1), y2))) MARK(s(cons(and(and(s(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(s(y0), y1), y2), y3))) MARK(s(cons(and(and(y0, y1), y2), y3))) -> c14(MARK(cons(and(and(y0, y1), y2), y3))) MARK(s(cons(and(length(zeros), y0), y1))) -> c14(MARK(cons(and(length(zeros), y0), y1))) MARK(s(cons(and(length(and(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(and(y0, y1)), y2), y3))) MARK(s(cons(and(length(length(y0)), y1), y2))) -> c14(MARK(cons(and(length(length(y0)), y1), y2))) MARK(s(cons(and(length(cons(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(cons(y0, y1)), y2), y3))) MARK(s(cons(and(length(s(y0)), y1), y2))) -> c14(MARK(cons(and(length(s(y0)), y1), y2))) MARK(s(cons(and(length(y0), y1), y2))) -> c14(MARK(cons(and(length(y0), y1), y2))) MARK(s(cons(and(and(zeros, y0), y1), y2))) -> c14(MARK(cons(and(and(zeros, y0), y1), y2))) MARK(s(cons(length(and(and(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(and(y0, y1), y2)), y3))) MARK(s(cons(length(and(length(y0), y1)), y2))) -> c14(MARK(cons(length(and(length(y0), y1)), y2))) MARK(s(cons(length(and(cons(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(cons(y0, y1), y2)), y3))) MARK(s(cons(length(and(tt, y0)), y1))) -> c14(MARK(cons(length(and(tt, y0)), y1))) MARK(s(cons(length(and(s(y0), y1)), y2))) -> c14(MARK(cons(length(and(s(y0), y1)), y2))) MARK(s(cons(length(and(y0, y1)), y2))) -> c14(MARK(cons(length(and(y0, y1)), y2))) MARK(s(cons(length(and(zeros, y0)), y1))) -> c14(MARK(cons(length(and(zeros, y0)), y1))) MARK(s(cons(length(length(zeros)), y0))) -> c14(MARK(cons(length(length(zeros)), y0))) MARK(s(cons(length(length(and(y0, y1))), y2))) -> c14(MARK(cons(length(length(and(y0, y1))), y2))) MARK(s(cons(length(length(length(y0))), y1))) -> c14(MARK(cons(length(length(length(y0))), y1))) MARK(s(cons(length(length(cons(y0, y1))), y2))) -> c14(MARK(cons(length(length(cons(y0, y1))), y2))) MARK(s(cons(length(length(s(y0))), y1))) -> c14(MARK(cons(length(length(s(y0))), y1))) MARK(s(cons(length(length(y0)), y1))) -> c14(MARK(cons(length(length(y0)), y1))) MARK(s(cons(length(zeros), y0))) -> c14(MARK(cons(length(zeros), y0))) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), 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c14(MARK(length(and(zeros, y0)))) MARK(s(length(length(zeros)))) -> c14(MARK(length(length(zeros)))) MARK(s(length(length(and(y0, y1))))) -> c14(MARK(length(length(and(y0, y1))))) MARK(s(length(length(length(y0))))) -> c14(MARK(length(length(length(y0))))) MARK(s(length(length(cons(y0, y1))))) -> c14(MARK(length(length(cons(y0, y1))))) MARK(s(length(length(s(y0))))) -> c14(MARK(length(length(s(y0))))) MARK(s(length(length(y0)))) -> c14(MARK(length(length(y0)))) MARK(s(length(zeros))) -> c14(MARK(length(zeros))) MARK(s(cons(cons(y0, y1), y2))) -> c14(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c14(MARK(cons(s(y0), y1))) MARK(s(cons(and(cons(y0, y1), y2), y3))) -> c14(MARK(cons(and(cons(y0, y1), y2), y3))) MARK(s(cons(and(tt, y0), y1))) -> c14(MARK(cons(and(tt, y0), y1))) MARK(s(cons(and(s(y0), y1), y2))) -> c14(MARK(cons(and(s(y0), y1), y2))) MARK(s(cons(length(cons(y0, y1)), y2))) -> c14(MARK(cons(length(cons(y0, y1)), y2))) MARK(s(cons(length(s(y0)), y1))) -> c14(MARK(cons(length(s(y0)), y1))) MARK(s(cons(and(and(and(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(and(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(length(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(length(y0), y1), y2), y3))) MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(cons(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(tt, y0), y1), y2))) -> c14(MARK(cons(and(and(tt, y0), y1), y2))) MARK(s(cons(and(and(s(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(s(y0), y1), y2), y3))) MARK(s(cons(and(and(y0, y1), y2), y3))) -> c14(MARK(cons(and(and(y0, y1), y2), y3))) MARK(s(cons(and(length(zeros), y0), y1))) -> c14(MARK(cons(and(length(zeros), y0), y1))) MARK(s(cons(and(length(and(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(and(y0, y1)), y2), y3))) MARK(s(cons(and(length(length(y0)), y1), y2))) -> c14(MARK(cons(and(length(length(y0)), y1), y2))) MARK(s(cons(and(length(cons(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(cons(y0, y1)), y2), y3))) MARK(s(cons(and(length(s(y0)), y1), y2))) -> c14(MARK(cons(and(length(s(y0)), y1), y2))) MARK(s(cons(and(length(y0), y1), y2))) -> c14(MARK(cons(and(length(y0), y1), y2))) MARK(s(cons(and(and(zeros, y0), y1), y2))) -> c14(MARK(cons(and(and(zeros, y0), y1), y2))) MARK(s(cons(length(and(and(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(and(y0, y1), y2)), y3))) MARK(s(cons(length(and(length(y0), y1)), y2))) -> c14(MARK(cons(length(and(length(y0), y1)), y2))) MARK(s(cons(length(and(cons(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(cons(y0, y1), y2)), y3))) MARK(s(cons(length(and(tt, y0)), y1))) -> c14(MARK(cons(length(and(tt, y0)), y1))) MARK(s(cons(length(and(s(y0), y1)), y2))) -> c14(MARK(cons(length(and(s(y0), y1)), y2))) MARK(s(cons(length(and(y0, y1)), y2))) -> c14(MARK(cons(length(and(y0, y1)), y2))) MARK(s(cons(length(and(zeros, y0)), y1))) -> c14(MARK(cons(length(and(zeros, y0)), y1))) MARK(s(cons(length(length(zeros)), y0))) -> c14(MARK(cons(length(length(zeros)), y0))) MARK(s(cons(length(length(and(y0, y1))), y2))) -> c14(MARK(cons(length(length(and(y0, y1))), y2))) MARK(s(cons(length(length(length(y0))), y1))) -> c14(MARK(cons(length(length(length(y0))), y1))) MARK(s(cons(length(length(cons(y0, y1))), y2))) -> c14(MARK(cons(length(length(cons(y0, y1))), y2))) MARK(s(cons(length(length(s(y0))), y1))) -> c14(MARK(cons(length(length(s(y0))), y1))) MARK(s(cons(length(length(y0)), y1))) -> c14(MARK(cons(length(length(y0)), y1))) MARK(s(cons(length(zeros), y0))) -> c14(MARK(cons(length(zeros), y0))) S tuples: A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) MARK(cons(and(and(cons(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(cons(y0, y1), y2), y3))) MARK(cons(and(and(tt, y0), y1), z1)) -> c10(MARK(and(and(tt, y0), y1))) MARK(cons(and(and(s(y0), y1), y2), z1)) -> c10(MARK(and(and(s(y0), y1), y2))) MARK(cons(and(and(y0, y1), y2), z1)) -> c10(MARK(and(and(y0, y1), y2))) MARK(cons(and(length(zeros), y0), z1)) -> c10(MARK(and(length(zeros), y0))) MARK(cons(and(length(and(y0, y1)), y2), z1)) -> c10(MARK(and(length(and(y0, y1)), y2))) MARK(cons(and(length(length(y0)), y1), z1)) -> c10(MARK(and(length(length(y0)), y1))) MARK(cons(and(length(cons(y0, y1)), y2), z1)) -> c10(MARK(and(length(cons(y0, y1)), y2))) MARK(cons(and(length(s(y0)), y1), z1)) -> c10(MARK(and(length(s(y0)), y1))) MARK(cons(and(length(y0), y1), z1)) -> c10(MARK(and(length(y0), y1))) MARK(cons(and(and(zeros, y0), y1), z1)) -> c10(MARK(and(and(zeros, y0), y1))) MARK(cons(length(and(and(y0, y1), y2)), z1)) -> c10(MARK(length(and(and(y0, y1), y2)))) MARK(cons(length(and(length(y0), y1)), z1)) -> c10(MARK(length(and(length(y0), y1)))) MARK(cons(length(and(cons(y0, y1), y2)), z1)) -> c10(MARK(length(and(cons(y0, y1), y2)))) MARK(cons(length(and(tt, y0)), z1)) -> c10(MARK(length(and(tt, y0)))) MARK(cons(length(and(s(y0), y1)), z1)) -> c10(MARK(length(and(s(y0), y1)))) MARK(cons(length(and(y0, y1)), z1)) -> c10(MARK(length(and(y0, y1)))) MARK(cons(length(and(zeros, y0)), z1)) -> c10(MARK(length(and(zeros, y0)))) MARK(cons(length(length(zeros)), z1)) -> c10(MARK(length(length(zeros)))) MARK(cons(length(length(and(y0, y1))), z1)) -> c10(MARK(length(length(and(y0, y1))))) MARK(cons(length(length(length(y0))), z1)) -> c10(MARK(length(length(length(y0))))) MARK(cons(length(length(cons(y0, y1))), z1)) -> c10(MARK(length(length(cons(y0, y1))))) MARK(cons(length(length(s(y0))), z1)) -> c10(MARK(length(length(s(y0))))) MARK(cons(length(length(y0)), z1)) -> c10(MARK(length(length(y0)))) MARK(cons(length(zeros), z1)) -> c10(MARK(length(zeros))) MARK(s(s(y0))) -> c14(MARK(s(y0))) MARK(s(and(cons(y0, y1), y2))) -> c14(MARK(and(cons(y0, y1), y2))) MARK(s(and(tt, y0))) -> c14(MARK(and(tt, y0))) MARK(s(and(s(y0), y1))) -> c14(MARK(and(s(y0), y1))) MARK(s(length(cons(y0, y1)))) -> c14(MARK(length(cons(y0, y1)))) MARK(s(length(s(y0)))) -> c14(MARK(length(s(y0)))) MARK(s(and(and(and(y0, y1), y2), y3))) -> c14(MARK(and(and(and(y0, y1), y2), y3))) MARK(s(and(and(length(y0), y1), y2))) -> c14(MARK(and(and(length(y0), y1), y2))) MARK(s(and(and(cons(y0, y1), y2), y3))) -> c14(MARK(and(and(cons(y0, y1), y2), y3))) MARK(s(and(and(tt, y0), y1))) -> c14(MARK(and(and(tt, y0), y1))) MARK(s(and(and(s(y0), y1), y2))) -> c14(MARK(and(and(s(y0), y1), y2))) MARK(s(and(and(y0, y1), y2))) -> c14(MARK(and(and(y0, y1), y2))) MARK(s(and(length(zeros), y0))) -> c14(MARK(and(length(zeros), y0))) MARK(s(and(length(and(y0, y1)), y2))) -> c14(MARK(and(length(and(y0, y1)), y2))) MARK(s(and(length(length(y0)), y1))) -> c14(MARK(and(length(length(y0)), y1))) MARK(s(and(length(cons(y0, y1)), y2))) -> c14(MARK(and(length(cons(y0, y1)), y2))) MARK(s(and(length(s(y0)), y1))) -> c14(MARK(and(length(s(y0)), y1))) MARK(s(and(length(y0), y1))) -> c14(MARK(and(length(y0), y1))) MARK(s(and(and(zeros, y0), y1))) -> c14(MARK(and(and(zeros, y0), y1))) MARK(s(length(and(and(y0, y1), y2)))) -> c14(MARK(length(and(and(y0, y1), y2)))) MARK(s(length(and(length(y0), y1)))) -> c14(MARK(length(and(length(y0), y1)))) MARK(s(length(and(cons(y0, y1), y2)))) -> c14(MARK(length(and(cons(y0, y1), y2)))) MARK(s(length(and(tt, y0)))) -> c14(MARK(length(and(tt, y0)))) MARK(s(length(and(s(y0), y1)))) -> c14(MARK(length(and(s(y0), y1)))) MARK(s(length(and(y0, y1)))) -> c14(MARK(length(and(y0, y1)))) MARK(s(length(and(zeros, y0)))) -> c14(MARK(length(and(zeros, y0)))) MARK(s(length(length(zeros)))) -> c14(MARK(length(length(zeros)))) MARK(s(length(length(and(y0, y1))))) -> c14(MARK(length(length(and(y0, y1))))) MARK(s(length(length(length(y0))))) -> c14(MARK(length(length(length(y0))))) MARK(s(length(length(cons(y0, y1))))) -> c14(MARK(length(length(cons(y0, y1))))) MARK(s(length(length(s(y0))))) -> c14(MARK(length(length(s(y0))))) MARK(s(length(length(y0)))) -> c14(MARK(length(length(y0)))) MARK(s(length(zeros))) -> c14(MARK(length(zeros))) MARK(s(cons(cons(y0, y1), y2))) -> c14(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c14(MARK(cons(s(y0), y1))) MARK(s(cons(and(cons(y0, y1), y2), y3))) -> c14(MARK(cons(and(cons(y0, y1), y2), y3))) MARK(s(cons(and(tt, y0), y1))) -> c14(MARK(cons(and(tt, y0), y1))) MARK(s(cons(and(s(y0), y1), y2))) -> c14(MARK(cons(and(s(y0), y1), y2))) MARK(s(cons(length(cons(y0, y1)), y2))) -> c14(MARK(cons(length(cons(y0, y1)), y2))) MARK(s(cons(length(s(y0)), y1))) -> c14(MARK(cons(length(s(y0)), y1))) MARK(s(cons(and(and(and(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(and(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(length(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(length(y0), y1), y2), y3))) MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(cons(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(tt, y0), y1), y2))) -> c14(MARK(cons(and(and(tt, y0), y1), y2))) MARK(s(cons(and(and(s(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(s(y0), y1), y2), y3))) MARK(s(cons(and(and(y0, y1), y2), y3))) -> c14(MARK(cons(and(and(y0, y1), y2), y3))) MARK(s(cons(and(length(zeros), y0), y1))) -> c14(MARK(cons(and(length(zeros), y0), y1))) MARK(s(cons(and(length(and(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(and(y0, y1)), y2), y3))) MARK(s(cons(and(length(length(y0)), y1), y2))) -> c14(MARK(cons(and(length(length(y0)), y1), y2))) MARK(s(cons(and(length(cons(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(cons(y0, y1)), y2), y3))) MARK(s(cons(and(length(s(y0)), y1), y2))) -> c14(MARK(cons(and(length(s(y0)), y1), y2))) MARK(s(cons(and(length(y0), y1), y2))) -> c14(MARK(cons(and(length(y0), y1), y2))) MARK(s(cons(and(and(zeros, y0), y1), y2))) -> c14(MARK(cons(and(and(zeros, y0), y1), y2))) MARK(s(cons(length(and(and(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(and(y0, y1), y2)), y3))) MARK(s(cons(length(and(length(y0), y1)), y2))) -> c14(MARK(cons(length(and(length(y0), y1)), y2))) MARK(s(cons(length(and(cons(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(cons(y0, y1), y2)), y3))) MARK(s(cons(length(and(tt, y0)), y1))) -> c14(MARK(cons(length(and(tt, y0)), y1))) MARK(s(cons(length(and(s(y0), y1)), y2))) -> c14(MARK(cons(length(and(s(y0), y1)), y2))) MARK(s(cons(length(and(y0, y1)), y2))) -> c14(MARK(cons(length(and(y0, y1)), y2))) MARK(s(cons(length(and(zeros, y0)), y1))) -> c14(MARK(cons(length(and(zeros, y0)), y1))) MARK(s(cons(length(length(zeros)), y0))) -> c14(MARK(cons(length(length(zeros)), y0))) MARK(s(cons(length(length(and(y0, y1))), y2))) -> c14(MARK(cons(length(length(and(y0, y1))), y2))) MARK(s(cons(length(length(length(y0))), y1))) -> c14(MARK(cons(length(length(length(y0))), y1))) MARK(s(cons(length(length(cons(y0, y1))), y2))) -> c14(MARK(cons(length(length(cons(y0, y1))), y2))) MARK(s(cons(length(length(s(y0))), y1))) -> c14(MARK(cons(length(length(s(y0))), y1))) MARK(s(cons(length(length(y0)), y1))) -> c14(MARK(cons(length(length(y0)), y1))) MARK(s(cons(length(zeros), y0))) -> c14(MARK(cons(length(zeros), y0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__LENGTH_1, MARK_1, A__AND_2 Compound Symbols: c5_2, c5_1, c8_1, c9_2, c9_1, c8_2, c2_1, c10_1, c14_1 ---------------------------------------- (171) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) by A__LENGTH(cons(z0, s(s(y0)))) -> c5(MARK(s(s(y0)))) A__LENGTH(cons(z0, s(and(cons(y0, y1), y2)))) -> c5(MARK(s(and(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(tt, y0)))) -> c5(MARK(s(and(tt, y0)))) A__LENGTH(cons(z0, s(and(s(y0), y1)))) -> c5(MARK(s(and(s(y0), y1)))) A__LENGTH(cons(z0, s(length(cons(y0, y1))))) -> c5(MARK(s(length(cons(y0, y1))))) A__LENGTH(cons(z0, s(length(s(y0))))) -> c5(MARK(s(length(s(y0))))) A__LENGTH(cons(z0, s(and(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(length(y0), y1), y2)))) -> c5(MARK(s(and(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(tt, y0), y1)))) -> c5(MARK(s(and(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(and(and(s(y0), y1), y2)))) -> c5(MARK(s(and(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(y0, y1), y2)))) -> c5(MARK(s(and(and(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(length(zeros), y0)))) -> c5(MARK(s(and(length(zeros), y0)))) A__LENGTH(cons(z0, s(and(length(and(y0, y1)), y2)))) -> c5(MARK(s(and(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(length(y0)), y1)))) -> c5(MARK(s(and(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(cons(y0, y1)), y2)))) -> c5(MARK(s(and(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(s(y0)), y1)))) -> c5(MARK(s(and(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(y0), y1)))) -> c5(MARK(s(and(length(y0), y1)))) A__LENGTH(cons(z0, s(and(and(zeros, y0), y1)))) -> c5(MARK(s(and(and(zeros, y0), y1)))) A__LENGTH(cons(z0, s(length(and(and(y0, y1), y2))))) -> c5(MARK(s(length(and(and(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(length(y0), y1))))) -> c5(MARK(s(length(and(length(y0), y1))))) A__LENGTH(cons(z0, s(length(and(cons(y0, y1), y2))))) -> c5(MARK(s(length(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(tt, y0))))) -> c5(MARK(s(length(and(tt, y0))))) A__LENGTH(cons(z0, s(length(and(s(y0), y1))))) -> c5(MARK(s(length(and(s(y0), y1))))) A__LENGTH(cons(z0, s(length(and(y0, y1))))) -> c5(MARK(s(length(and(y0, y1))))) A__LENGTH(cons(z0, s(length(and(zeros, y0))))) -> c5(MARK(s(length(and(zeros, y0))))) A__LENGTH(cons(z0, s(length(length(zeros))))) -> c5(MARK(s(length(length(zeros))))) A__LENGTH(cons(z0, s(length(length(and(y0, y1)))))) -> c5(MARK(s(length(length(and(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(length(y0)))))) -> c5(MARK(s(length(length(length(y0)))))) A__LENGTH(cons(z0, s(length(length(cons(y0, y1)))))) -> c5(MARK(s(length(length(cons(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(s(y0)))))) -> c5(MARK(s(length(length(s(y0)))))) A__LENGTH(cons(z0, s(length(length(y0))))) -> c5(MARK(s(length(length(y0))))) A__LENGTH(cons(z0, s(length(zeros)))) -> c5(MARK(s(length(zeros)))) A__LENGTH(cons(z0, s(cons(cons(y0, y1), y2)))) -> c5(MARK(s(cons(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(cons(s(y0), y1)))) -> c5(MARK(s(cons(s(y0), y1)))) A__LENGTH(cons(z0, s(cons(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(tt, y0), y1)))) -> c5(MARK(s(cons(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(cons(and(s(y0), y1), y2)))) -> c5(MARK(s(cons(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(length(cons(y0, y1)), y2)))) -> c5(MARK(s(cons(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(s(y0)), y1)))) -> c5(MARK(s(cons(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(cons(and(and(and(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(and(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(length(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(length(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(cons(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(tt, y0), y1), y2)))) -> c5(MARK(s(cons(and(and(tt, y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(and(s(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(s(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(zeros), y0), y1)))) -> c5(MARK(s(cons(and(length(zeros), y0), y1)))) A__LENGTH(cons(z0, s(cons(and(length(and(y0, y1)), y2), y3)))) -> c5(MARK(s(cons(and(length(and(y0, y1)), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(length(y0)), y1), y2)))) -> c5(MARK(s(cons(and(length(length(y0)), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(length(cons(y0, y1)), y2), y3)))) -> c5(MARK(s(cons(and(length(cons(y0, y1)), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(s(y0)), y1), y2)))) -> c5(MARK(s(cons(and(length(s(y0)), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(length(y0), y1), y2)))) -> c5(MARK(s(cons(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(and(zeros, y0), y1), y2)))) -> c5(MARK(s(cons(and(and(zeros, y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(length(and(and(y0, y1), y2)), y3)))) -> c5(MARK(s(cons(length(and(and(y0, y1), y2)), y3)))) A__LENGTH(cons(z0, s(cons(length(and(length(y0), y1)), y2)))) -> c5(MARK(s(cons(length(and(length(y0), y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(cons(y0, y1), y2)), y3)))) -> c5(MARK(s(cons(length(and(cons(y0, y1), y2)), y3)))) A__LENGTH(cons(z0, s(cons(length(and(tt, y0)), y1)))) -> c5(MARK(s(cons(length(and(tt, y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(and(s(y0), y1)), y2)))) -> c5(MARK(s(cons(length(and(s(y0), y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(y0, y1)), y2)))) -> c5(MARK(s(cons(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(zeros, y0)), y1)))) -> c5(MARK(s(cons(length(and(zeros, y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(length(zeros)), y0)))) -> c5(MARK(s(cons(length(length(zeros)), y0)))) A__LENGTH(cons(z0, s(cons(length(length(and(y0, y1))), y2)))) -> c5(MARK(s(cons(length(length(and(y0, y1))), y2)))) A__LENGTH(cons(z0, s(cons(length(length(length(y0))), y1)))) -> c5(MARK(s(cons(length(length(length(y0))), y1)))) A__LENGTH(cons(z0, s(cons(length(length(cons(y0, y1))), y2)))) -> c5(MARK(s(cons(length(length(cons(y0, y1))), y2)))) A__LENGTH(cons(z0, s(cons(length(length(s(y0))), y1)))) -> c5(MARK(s(cons(length(length(s(y0))), y1)))) A__LENGTH(cons(z0, s(cons(length(length(y0)), y1)))) -> c5(MARK(s(cons(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(zeros), y0)))) -> c5(MARK(s(cons(length(zeros), y0)))) ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) MARK(cons(and(and(cons(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(cons(y0, y1), y2), y3))) MARK(cons(and(and(tt, y0), y1), z1)) -> c10(MARK(and(and(tt, y0), y1))) MARK(cons(and(and(s(y0), y1), y2), z1)) -> c10(MARK(and(and(s(y0), y1), y2))) MARK(cons(and(and(y0, y1), y2), z1)) -> c10(MARK(and(and(y0, y1), y2))) MARK(cons(and(length(zeros), y0), z1)) -> c10(MARK(and(length(zeros), y0))) MARK(cons(and(length(and(y0, y1)), y2), z1)) -> c10(MARK(and(length(and(y0, y1)), y2))) MARK(cons(and(length(length(y0)), y1), z1)) -> c10(MARK(and(length(length(y0)), y1))) MARK(cons(and(length(cons(y0, y1)), y2), z1)) -> c10(MARK(and(length(cons(y0, y1)), y2))) MARK(cons(and(length(s(y0)), y1), z1)) -> c10(MARK(and(length(s(y0)), y1))) MARK(cons(and(length(y0), y1), z1)) -> c10(MARK(and(length(y0), y1))) MARK(cons(and(and(zeros, y0), y1), z1)) -> c10(MARK(and(and(zeros, y0), y1))) MARK(cons(length(and(and(y0, y1), y2)), z1)) -> c10(MARK(length(and(and(y0, y1), y2)))) MARK(cons(length(and(length(y0), y1)), z1)) -> c10(MARK(length(and(length(y0), y1)))) MARK(cons(length(and(cons(y0, y1), y2)), z1)) -> c10(MARK(length(and(cons(y0, y1), y2)))) MARK(cons(length(and(tt, y0)), z1)) -> c10(MARK(length(and(tt, y0)))) MARK(cons(length(and(s(y0), y1)), z1)) -> c10(MARK(length(and(s(y0), y1)))) MARK(cons(length(and(y0, y1)), z1)) -> c10(MARK(length(and(y0, y1)))) MARK(cons(length(and(zeros, y0)), z1)) -> c10(MARK(length(and(zeros, y0)))) MARK(cons(length(length(zeros)), z1)) -> c10(MARK(length(length(zeros)))) MARK(cons(length(length(and(y0, y1))), z1)) -> c10(MARK(length(length(and(y0, y1))))) MARK(cons(length(length(length(y0))), z1)) -> c10(MARK(length(length(length(y0))))) MARK(cons(length(length(cons(y0, y1))), z1)) -> c10(MARK(length(length(cons(y0, y1))))) MARK(cons(length(length(s(y0))), z1)) -> c10(MARK(length(length(s(y0))))) MARK(cons(length(length(y0)), z1)) -> c10(MARK(length(length(y0)))) MARK(cons(length(zeros), z1)) -> c10(MARK(length(zeros))) MARK(s(s(y0))) -> c14(MARK(s(y0))) MARK(s(and(cons(y0, y1), y2))) -> c14(MARK(and(cons(y0, y1), y2))) MARK(s(and(tt, y0))) -> c14(MARK(and(tt, y0))) MARK(s(and(s(y0), y1))) -> c14(MARK(and(s(y0), y1))) MARK(s(length(cons(y0, y1)))) -> c14(MARK(length(cons(y0, y1)))) MARK(s(length(s(y0)))) -> c14(MARK(length(s(y0)))) MARK(s(and(and(and(y0, y1), y2), y3))) -> c14(MARK(and(and(and(y0, y1), y2), y3))) MARK(s(and(and(length(y0), y1), y2))) -> c14(MARK(and(and(length(y0), y1), y2))) MARK(s(and(and(cons(y0, y1), y2), y3))) -> c14(MARK(and(and(cons(y0, y1), y2), y3))) MARK(s(and(and(tt, y0), y1))) -> c14(MARK(and(and(tt, y0), y1))) MARK(s(and(and(s(y0), y1), y2))) -> c14(MARK(and(and(s(y0), y1), y2))) MARK(s(and(and(y0, y1), y2))) -> c14(MARK(and(and(y0, y1), y2))) MARK(s(and(length(zeros), y0))) -> c14(MARK(and(length(zeros), y0))) MARK(s(and(length(and(y0, y1)), y2))) -> c14(MARK(and(length(and(y0, y1)), y2))) MARK(s(and(length(length(y0)), y1))) -> c14(MARK(and(length(length(y0)), y1))) MARK(s(and(length(cons(y0, y1)), y2))) -> c14(MARK(and(length(cons(y0, y1)), y2))) MARK(s(and(length(s(y0)), y1))) -> c14(MARK(and(length(s(y0)), y1))) MARK(s(and(length(y0), y1))) -> c14(MARK(and(length(y0), y1))) MARK(s(and(and(zeros, y0), y1))) -> c14(MARK(and(and(zeros, y0), y1))) MARK(s(length(and(and(y0, y1), y2)))) -> c14(MARK(length(and(and(y0, y1), y2)))) MARK(s(length(and(length(y0), y1)))) -> c14(MARK(length(and(length(y0), y1)))) MARK(s(length(and(cons(y0, y1), y2)))) -> c14(MARK(length(and(cons(y0, y1), y2)))) MARK(s(length(and(tt, y0)))) -> c14(MARK(length(and(tt, y0)))) MARK(s(length(and(s(y0), y1)))) -> c14(MARK(length(and(s(y0), y1)))) MARK(s(length(and(y0, y1)))) -> c14(MARK(length(and(y0, y1)))) MARK(s(length(and(zeros, y0)))) -> c14(MARK(length(and(zeros, y0)))) MARK(s(length(length(zeros)))) -> c14(MARK(length(length(zeros)))) MARK(s(length(length(and(y0, y1))))) -> c14(MARK(length(length(and(y0, y1))))) MARK(s(length(length(length(y0))))) -> c14(MARK(length(length(length(y0))))) MARK(s(length(length(cons(y0, y1))))) -> c14(MARK(length(length(cons(y0, y1))))) MARK(s(length(length(s(y0))))) -> c14(MARK(length(length(s(y0))))) MARK(s(length(length(y0)))) -> c14(MARK(length(length(y0)))) MARK(s(length(zeros))) -> c14(MARK(length(zeros))) MARK(s(cons(cons(y0, y1), y2))) -> c14(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c14(MARK(cons(s(y0), y1))) MARK(s(cons(and(cons(y0, y1), y2), y3))) -> c14(MARK(cons(and(cons(y0, y1), y2), y3))) MARK(s(cons(and(tt, y0), y1))) -> c14(MARK(cons(and(tt, y0), y1))) MARK(s(cons(and(s(y0), y1), y2))) -> c14(MARK(cons(and(s(y0), y1), y2))) MARK(s(cons(length(cons(y0, y1)), y2))) -> c14(MARK(cons(length(cons(y0, y1)), y2))) MARK(s(cons(length(s(y0)), y1))) -> c14(MARK(cons(length(s(y0)), y1))) MARK(s(cons(and(and(and(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(and(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(length(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(length(y0), y1), y2), y3))) MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(cons(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(tt, y0), y1), y2))) -> c14(MARK(cons(and(and(tt, y0), y1), y2))) MARK(s(cons(and(and(s(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(s(y0), y1), y2), y3))) MARK(s(cons(and(and(y0, y1), y2), y3))) -> c14(MARK(cons(and(and(y0, y1), y2), y3))) MARK(s(cons(and(length(zeros), y0), y1))) -> c14(MARK(cons(and(length(zeros), y0), y1))) MARK(s(cons(and(length(and(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(and(y0, y1)), y2), y3))) MARK(s(cons(and(length(length(y0)), y1), y2))) -> c14(MARK(cons(and(length(length(y0)), y1), y2))) MARK(s(cons(and(length(cons(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(cons(y0, y1)), y2), y3))) MARK(s(cons(and(length(s(y0)), y1), y2))) -> c14(MARK(cons(and(length(s(y0)), y1), y2))) MARK(s(cons(and(length(y0), y1), y2))) -> c14(MARK(cons(and(length(y0), y1), y2))) MARK(s(cons(and(and(zeros, y0), y1), y2))) -> c14(MARK(cons(and(and(zeros, y0), y1), y2))) MARK(s(cons(length(and(and(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(and(y0, y1), y2)), y3))) MARK(s(cons(length(and(length(y0), y1)), y2))) -> c14(MARK(cons(length(and(length(y0), y1)), y2))) MARK(s(cons(length(and(cons(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(cons(y0, y1), y2)), y3))) MARK(s(cons(length(and(tt, y0)), y1))) -> c14(MARK(cons(length(and(tt, y0)), y1))) MARK(s(cons(length(and(s(y0), y1)), y2))) -> c14(MARK(cons(length(and(s(y0), y1)), y2))) MARK(s(cons(length(and(y0, y1)), y2))) -> c14(MARK(cons(length(and(y0, y1)), y2))) MARK(s(cons(length(and(zeros, y0)), y1))) -> c14(MARK(cons(length(and(zeros, y0)), y1))) MARK(s(cons(length(length(zeros)), y0))) -> c14(MARK(cons(length(length(zeros)), y0))) MARK(s(cons(length(length(and(y0, y1))), y2))) -> c14(MARK(cons(length(length(and(y0, y1))), y2))) MARK(s(cons(length(length(length(y0))), y1))) -> c14(MARK(cons(length(length(length(y0))), y1))) MARK(s(cons(length(length(cons(y0, y1))), y2))) -> c14(MARK(cons(length(length(cons(y0, y1))), y2))) MARK(s(cons(length(length(s(y0))), y1))) -> c14(MARK(cons(length(length(s(y0))), y1))) MARK(s(cons(length(length(y0)), y1))) -> c14(MARK(cons(length(length(y0)), y1))) MARK(s(cons(length(zeros), y0))) -> c14(MARK(cons(length(zeros), y0))) A__LENGTH(cons(z0, s(s(y0)))) -> c5(MARK(s(s(y0)))) A__LENGTH(cons(z0, s(and(cons(y0, y1), y2)))) -> c5(MARK(s(and(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(tt, y0)))) -> c5(MARK(s(and(tt, y0)))) A__LENGTH(cons(z0, s(and(s(y0), y1)))) -> c5(MARK(s(and(s(y0), y1)))) A__LENGTH(cons(z0, s(length(cons(y0, y1))))) -> c5(MARK(s(length(cons(y0, y1))))) A__LENGTH(cons(z0, s(length(s(y0))))) -> c5(MARK(s(length(s(y0))))) A__LENGTH(cons(z0, s(and(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(length(y0), y1), y2)))) -> c5(MARK(s(and(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(tt, y0), y1)))) -> c5(MARK(s(and(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(and(and(s(y0), y1), y2)))) -> c5(MARK(s(and(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(y0, y1), y2)))) -> c5(MARK(s(and(and(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(length(zeros), y0)))) -> c5(MARK(s(and(length(zeros), y0)))) A__LENGTH(cons(z0, s(and(length(and(y0, y1)), y2)))) -> c5(MARK(s(and(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(length(y0)), y1)))) -> c5(MARK(s(and(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(cons(y0, y1)), y2)))) -> c5(MARK(s(and(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(s(y0)), y1)))) -> c5(MARK(s(and(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(y0), y1)))) -> c5(MARK(s(and(length(y0), y1)))) A__LENGTH(cons(z0, s(and(and(zeros, y0), y1)))) -> c5(MARK(s(and(and(zeros, y0), y1)))) A__LENGTH(cons(z0, s(length(and(and(y0, y1), y2))))) -> c5(MARK(s(length(and(and(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(length(y0), y1))))) -> c5(MARK(s(length(and(length(y0), y1))))) A__LENGTH(cons(z0, s(length(and(cons(y0, y1), y2))))) -> c5(MARK(s(length(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(tt, y0))))) -> c5(MARK(s(length(and(tt, y0))))) A__LENGTH(cons(z0, s(length(and(s(y0), y1))))) -> c5(MARK(s(length(and(s(y0), y1))))) A__LENGTH(cons(z0, s(length(and(y0, y1))))) -> c5(MARK(s(length(and(y0, y1))))) A__LENGTH(cons(z0, s(length(and(zeros, y0))))) -> c5(MARK(s(length(and(zeros, y0))))) A__LENGTH(cons(z0, s(length(length(zeros))))) -> c5(MARK(s(length(length(zeros))))) A__LENGTH(cons(z0, s(length(length(and(y0, y1)))))) -> c5(MARK(s(length(length(and(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(length(y0)))))) -> c5(MARK(s(length(length(length(y0)))))) A__LENGTH(cons(z0, s(length(length(cons(y0, y1)))))) -> c5(MARK(s(length(length(cons(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(s(y0)))))) -> c5(MARK(s(length(length(s(y0)))))) A__LENGTH(cons(z0, s(length(length(y0))))) -> c5(MARK(s(length(length(y0))))) A__LENGTH(cons(z0, s(length(zeros)))) -> c5(MARK(s(length(zeros)))) A__LENGTH(cons(z0, s(cons(cons(y0, y1), y2)))) -> c5(MARK(s(cons(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(cons(s(y0), y1)))) -> c5(MARK(s(cons(s(y0), y1)))) A__LENGTH(cons(z0, s(cons(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(tt, y0), y1)))) -> c5(MARK(s(cons(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(cons(and(s(y0), y1), y2)))) -> c5(MARK(s(cons(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(length(cons(y0, y1)), y2)))) -> c5(MARK(s(cons(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(s(y0)), y1)))) -> c5(MARK(s(cons(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(cons(and(and(and(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(and(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(length(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(length(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(cons(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(tt, y0), y1), y2)))) -> c5(MARK(s(cons(and(and(tt, y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(and(s(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(s(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(zeros), y0), y1)))) -> c5(MARK(s(cons(and(length(zeros), y0), y1)))) A__LENGTH(cons(z0, s(cons(and(length(and(y0, y1)), y2), y3)))) -> c5(MARK(s(cons(and(length(and(y0, y1)), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(length(y0)), y1), y2)))) -> c5(MARK(s(cons(and(length(length(y0)), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(length(cons(y0, y1)), y2), y3)))) -> c5(MARK(s(cons(and(length(cons(y0, y1)), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(s(y0)), y1), y2)))) -> c5(MARK(s(cons(and(length(s(y0)), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(length(y0), y1), y2)))) -> c5(MARK(s(cons(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(and(zeros, y0), y1), y2)))) -> c5(MARK(s(cons(and(and(zeros, y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(length(and(and(y0, y1), y2)), y3)))) -> c5(MARK(s(cons(length(and(and(y0, y1), y2)), y3)))) A__LENGTH(cons(z0, s(cons(length(and(length(y0), y1)), y2)))) -> c5(MARK(s(cons(length(and(length(y0), y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(cons(y0, y1), y2)), y3)))) -> c5(MARK(s(cons(length(and(cons(y0, y1), y2)), y3)))) A__LENGTH(cons(z0, s(cons(length(and(tt, y0)), y1)))) -> c5(MARK(s(cons(length(and(tt, y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(and(s(y0), y1)), y2)))) -> c5(MARK(s(cons(length(and(s(y0), y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(y0, y1)), y2)))) -> c5(MARK(s(cons(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(zeros, y0)), y1)))) -> c5(MARK(s(cons(length(and(zeros, y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(length(zeros)), y0)))) -> c5(MARK(s(cons(length(length(zeros)), y0)))) A__LENGTH(cons(z0, s(cons(length(length(and(y0, y1))), y2)))) -> c5(MARK(s(cons(length(length(and(y0, y1))), y2)))) A__LENGTH(cons(z0, s(cons(length(length(length(y0))), y1)))) -> c5(MARK(s(cons(length(length(length(y0))), y1)))) A__LENGTH(cons(z0, s(cons(length(length(cons(y0, y1))), y2)))) -> c5(MARK(s(cons(length(length(cons(y0, y1))), y2)))) A__LENGTH(cons(z0, s(cons(length(length(s(y0))), y1)))) -> c5(MARK(s(cons(length(length(s(y0))), y1)))) A__LENGTH(cons(z0, s(cons(length(length(y0)), y1)))) -> c5(MARK(s(cons(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(zeros), y0)))) -> c5(MARK(s(cons(length(zeros), y0)))) S tuples: A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) MARK(cons(and(and(cons(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(cons(y0, y1), y2), y3))) MARK(cons(and(and(tt, y0), y1), z1)) -> c10(MARK(and(and(tt, y0), y1))) MARK(cons(and(and(s(y0), y1), y2), z1)) -> c10(MARK(and(and(s(y0), y1), y2))) MARK(cons(and(and(y0, y1), y2), z1)) -> c10(MARK(and(and(y0, y1), y2))) MARK(cons(and(length(zeros), y0), z1)) -> c10(MARK(and(length(zeros), y0))) MARK(cons(and(length(and(y0, y1)), y2), z1)) -> c10(MARK(and(length(and(y0, y1)), y2))) MARK(cons(and(length(length(y0)), y1), z1)) -> c10(MARK(and(length(length(y0)), y1))) MARK(cons(and(length(cons(y0, y1)), y2), z1)) -> c10(MARK(and(length(cons(y0, y1)), y2))) MARK(cons(and(length(s(y0)), y1), z1)) -> c10(MARK(and(length(s(y0)), y1))) MARK(cons(and(length(y0), y1), z1)) -> c10(MARK(and(length(y0), y1))) MARK(cons(and(and(zeros, y0), y1), z1)) -> c10(MARK(and(and(zeros, y0), y1))) MARK(cons(length(and(and(y0, y1), y2)), z1)) -> c10(MARK(length(and(and(y0, y1), y2)))) MARK(cons(length(and(length(y0), y1)), z1)) -> c10(MARK(length(and(length(y0), y1)))) MARK(cons(length(and(cons(y0, y1), y2)), z1)) -> c10(MARK(length(and(cons(y0, y1), y2)))) MARK(cons(length(and(tt, y0)), z1)) -> c10(MARK(length(and(tt, y0)))) MARK(cons(length(and(s(y0), y1)), z1)) -> c10(MARK(length(and(s(y0), y1)))) MARK(cons(length(and(y0, y1)), z1)) -> c10(MARK(length(and(y0, y1)))) MARK(cons(length(and(zeros, y0)), z1)) -> c10(MARK(length(and(zeros, 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c14(MARK(and(and(length(y0), y1), y2))) MARK(s(and(and(cons(y0, y1), y2), y3))) -> c14(MARK(and(and(cons(y0, y1), y2), y3))) MARK(s(and(and(tt, y0), y1))) -> c14(MARK(and(and(tt, y0), y1))) MARK(s(and(and(s(y0), y1), y2))) -> c14(MARK(and(and(s(y0), y1), y2))) MARK(s(and(and(y0, y1), y2))) -> c14(MARK(and(and(y0, y1), y2))) MARK(s(and(length(zeros), y0))) -> c14(MARK(and(length(zeros), y0))) MARK(s(and(length(and(y0, y1)), y2))) -> c14(MARK(and(length(and(y0, y1)), y2))) MARK(s(and(length(length(y0)), y1))) -> c14(MARK(and(length(length(y0)), y1))) MARK(s(and(length(cons(y0, y1)), y2))) -> c14(MARK(and(length(cons(y0, y1)), y2))) MARK(s(and(length(s(y0)), y1))) -> c14(MARK(and(length(s(y0)), y1))) MARK(s(and(length(y0), y1))) -> c14(MARK(and(length(y0), y1))) MARK(s(and(and(zeros, y0), y1))) -> c14(MARK(and(and(zeros, y0), y1))) MARK(s(length(and(and(y0, y1), y2)))) -> c14(MARK(length(and(and(y0, y1), y2)))) MARK(s(length(and(length(y0), y1)))) -> c14(MARK(length(and(length(y0), y1)))) MARK(s(length(and(cons(y0, y1), y2)))) -> c14(MARK(length(and(cons(y0, y1), y2)))) MARK(s(length(and(tt, y0)))) -> c14(MARK(length(and(tt, y0)))) MARK(s(length(and(s(y0), y1)))) -> c14(MARK(length(and(s(y0), y1)))) MARK(s(length(and(y0, y1)))) -> c14(MARK(length(and(y0, y1)))) MARK(s(length(and(zeros, y0)))) -> c14(MARK(length(and(zeros, y0)))) MARK(s(length(length(zeros)))) -> c14(MARK(length(length(zeros)))) MARK(s(length(length(and(y0, y1))))) -> c14(MARK(length(length(and(y0, y1))))) MARK(s(length(length(length(y0))))) -> c14(MARK(length(length(length(y0))))) MARK(s(length(length(cons(y0, y1))))) -> c14(MARK(length(length(cons(y0, y1))))) MARK(s(length(length(s(y0))))) -> c14(MARK(length(length(s(y0))))) MARK(s(length(length(y0)))) -> c14(MARK(length(length(y0)))) MARK(s(length(zeros))) -> c14(MARK(length(zeros))) MARK(s(cons(cons(y0, y1), y2))) -> c14(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c14(MARK(cons(s(y0), y1))) MARK(s(cons(and(cons(y0, y1), y2), y3))) -> c14(MARK(cons(and(cons(y0, y1), y2), y3))) MARK(s(cons(and(tt, y0), y1))) -> c14(MARK(cons(and(tt, y0), y1))) MARK(s(cons(and(s(y0), y1), y2))) -> c14(MARK(cons(and(s(y0), y1), y2))) MARK(s(cons(length(cons(y0, y1)), y2))) -> c14(MARK(cons(length(cons(y0, y1)), y2))) MARK(s(cons(length(s(y0)), y1))) -> c14(MARK(cons(length(s(y0)), y1))) MARK(s(cons(and(and(and(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(and(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(length(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(length(y0), y1), y2), y3))) MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(cons(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(tt, y0), y1), y2))) -> c14(MARK(cons(and(and(tt, y0), y1), y2))) MARK(s(cons(and(and(s(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(s(y0), y1), y2), y3))) MARK(s(cons(and(and(y0, y1), y2), y3))) -> c14(MARK(cons(and(and(y0, y1), y2), y3))) MARK(s(cons(and(length(zeros), y0), y1))) -> c14(MARK(cons(and(length(zeros), y0), y1))) MARK(s(cons(and(length(and(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(and(y0, y1)), y2), y3))) MARK(s(cons(and(length(length(y0)), y1), y2))) -> c14(MARK(cons(and(length(length(y0)), y1), y2))) MARK(s(cons(and(length(cons(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(cons(y0, y1)), y2), y3))) MARK(s(cons(and(length(s(y0)), y1), y2))) -> c14(MARK(cons(and(length(s(y0)), y1), y2))) MARK(s(cons(and(length(y0), y1), y2))) -> c14(MARK(cons(and(length(y0), y1), y2))) MARK(s(cons(and(and(zeros, y0), y1), y2))) -> c14(MARK(cons(and(and(zeros, y0), y1), y2))) MARK(s(cons(length(and(and(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(and(y0, y1), y2)), y3))) MARK(s(cons(length(and(length(y0), y1)), y2))) -> c14(MARK(cons(length(and(length(y0), y1)), y2))) MARK(s(cons(length(and(cons(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(cons(y0, y1), y2)), y3))) MARK(s(cons(length(and(tt, y0)), y1))) -> c14(MARK(cons(length(and(tt, y0)), y1))) MARK(s(cons(length(and(s(y0), y1)), y2))) -> c14(MARK(cons(length(and(s(y0), y1)), y2))) MARK(s(cons(length(and(y0, y1)), y2))) -> c14(MARK(cons(length(and(y0, y1)), y2))) MARK(s(cons(length(and(zeros, y0)), y1))) -> c14(MARK(cons(length(and(zeros, y0)), y1))) MARK(s(cons(length(length(zeros)), y0))) -> c14(MARK(cons(length(length(zeros)), y0))) MARK(s(cons(length(length(and(y0, y1))), y2))) -> c14(MARK(cons(length(length(and(y0, y1))), y2))) MARK(s(cons(length(length(length(y0))), y1))) -> c14(MARK(cons(length(length(length(y0))), y1))) MARK(s(cons(length(length(cons(y0, y1))), y2))) -> c14(MARK(cons(length(length(cons(y0, y1))), y2))) MARK(s(cons(length(length(s(y0))), y1))) -> c14(MARK(cons(length(length(s(y0))), y1))) MARK(s(cons(length(length(y0)), y1))) -> c14(MARK(cons(length(length(y0)), y1))) MARK(s(cons(length(zeros), y0))) -> c14(MARK(cons(length(zeros), y0))) A__LENGTH(cons(z0, s(s(y0)))) -> c5(MARK(s(s(y0)))) A__LENGTH(cons(z0, s(and(cons(y0, y1), y2)))) -> c5(MARK(s(and(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(tt, y0)))) -> c5(MARK(s(and(tt, y0)))) A__LENGTH(cons(z0, s(and(s(y0), y1)))) -> c5(MARK(s(and(s(y0), y1)))) A__LENGTH(cons(z0, s(length(cons(y0, y1))))) -> c5(MARK(s(length(cons(y0, y1))))) A__LENGTH(cons(z0, s(length(s(y0))))) -> c5(MARK(s(length(s(y0))))) A__LENGTH(cons(z0, s(and(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(length(y0), y1), y2)))) -> c5(MARK(s(and(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(tt, y0), y1)))) -> c5(MARK(s(and(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(and(and(s(y0), y1), y2)))) -> c5(MARK(s(and(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(y0, y1), y2)))) -> c5(MARK(s(and(and(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(length(zeros), y0)))) -> c5(MARK(s(and(length(zeros), y0)))) A__LENGTH(cons(z0, s(and(length(and(y0, y1)), y2)))) -> c5(MARK(s(and(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(length(y0)), y1)))) -> c5(MARK(s(and(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(cons(y0, y1)), y2)))) -> c5(MARK(s(and(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(s(y0)), y1)))) -> c5(MARK(s(and(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(y0), y1)))) -> c5(MARK(s(and(length(y0), y1)))) A__LENGTH(cons(z0, s(and(and(zeros, y0), y1)))) -> c5(MARK(s(and(and(zeros, y0), y1)))) A__LENGTH(cons(z0, s(length(and(and(y0, y1), y2))))) -> c5(MARK(s(length(and(and(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(length(y0), y1))))) -> c5(MARK(s(length(and(length(y0), y1))))) A__LENGTH(cons(z0, s(length(and(cons(y0, y1), y2))))) -> c5(MARK(s(length(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(tt, y0))))) -> c5(MARK(s(length(and(tt, y0))))) A__LENGTH(cons(z0, s(length(and(s(y0), y1))))) -> c5(MARK(s(length(and(s(y0), y1))))) A__LENGTH(cons(z0, s(length(and(y0, y1))))) -> c5(MARK(s(length(and(y0, y1))))) A__LENGTH(cons(z0, s(length(and(zeros, y0))))) -> c5(MARK(s(length(and(zeros, y0))))) A__LENGTH(cons(z0, s(length(length(zeros))))) -> c5(MARK(s(length(length(zeros))))) A__LENGTH(cons(z0, s(length(length(and(y0, y1)))))) -> c5(MARK(s(length(length(and(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(length(y0)))))) -> c5(MARK(s(length(length(length(y0)))))) A__LENGTH(cons(z0, s(length(length(cons(y0, y1)))))) -> c5(MARK(s(length(length(cons(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(s(y0)))))) -> c5(MARK(s(length(length(s(y0)))))) A__LENGTH(cons(z0, s(length(length(y0))))) -> c5(MARK(s(length(length(y0))))) A__LENGTH(cons(z0, s(length(zeros)))) -> c5(MARK(s(length(zeros)))) A__LENGTH(cons(z0, s(cons(cons(y0, y1), y2)))) -> c5(MARK(s(cons(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(cons(s(y0), y1)))) -> c5(MARK(s(cons(s(y0), y1)))) A__LENGTH(cons(z0, s(cons(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(tt, y0), y1)))) -> c5(MARK(s(cons(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(cons(and(s(y0), y1), y2)))) -> c5(MARK(s(cons(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(length(cons(y0, y1)), y2)))) -> c5(MARK(s(cons(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(s(y0)), y1)))) -> c5(MARK(s(cons(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(cons(and(and(and(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(and(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(length(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(length(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(cons(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(tt, y0), y1), y2)))) -> c5(MARK(s(cons(and(and(tt, y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(and(s(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(s(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(zeros), y0), y1)))) -> c5(MARK(s(cons(and(length(zeros), y0), y1)))) A__LENGTH(cons(z0, s(cons(and(length(and(y0, y1)), y2), y3)))) -> c5(MARK(s(cons(and(length(and(y0, y1)), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(length(y0)), y1), y2)))) -> c5(MARK(s(cons(and(length(length(y0)), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(length(cons(y0, y1)), y2), y3)))) -> c5(MARK(s(cons(and(length(cons(y0, y1)), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(s(y0)), y1), y2)))) -> c5(MARK(s(cons(and(length(s(y0)), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(length(y0), y1), y2)))) -> c5(MARK(s(cons(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(and(zeros, y0), y1), y2)))) -> c5(MARK(s(cons(and(and(zeros, y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(length(and(and(y0, y1), y2)), y3)))) -> c5(MARK(s(cons(length(and(and(y0, y1), y2)), y3)))) A__LENGTH(cons(z0, s(cons(length(and(length(y0), y1)), y2)))) -> c5(MARK(s(cons(length(and(length(y0), y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(cons(y0, y1), y2)), y3)))) -> c5(MARK(s(cons(length(and(cons(y0, y1), y2)), y3)))) A__LENGTH(cons(z0, s(cons(length(and(tt, y0)), y1)))) -> c5(MARK(s(cons(length(and(tt, y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(and(s(y0), y1)), y2)))) -> c5(MARK(s(cons(length(and(s(y0), y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(y0, y1)), y2)))) -> c5(MARK(s(cons(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(zeros, y0)), y1)))) -> c5(MARK(s(cons(length(and(zeros, y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(length(zeros)), y0)))) -> c5(MARK(s(cons(length(length(zeros)), y0)))) A__LENGTH(cons(z0, s(cons(length(length(and(y0, y1))), y2)))) -> c5(MARK(s(cons(length(length(and(y0, y1))), y2)))) A__LENGTH(cons(z0, s(cons(length(length(length(y0))), y1)))) -> c5(MARK(s(cons(length(length(length(y0))), y1)))) A__LENGTH(cons(z0, s(cons(length(length(cons(y0, y1))), y2)))) -> c5(MARK(s(cons(length(length(cons(y0, y1))), y2)))) A__LENGTH(cons(z0, s(cons(length(length(s(y0))), y1)))) -> c5(MARK(s(cons(length(length(s(y0))), y1)))) A__LENGTH(cons(z0, s(cons(length(length(y0)), y1)))) -> c5(MARK(s(cons(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(zeros), y0)))) -> c5(MARK(s(cons(length(zeros), y0)))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__LENGTH_1, MARK_1, A__AND_2 Compound Symbols: c5_2, c8_1, c9_2, c9_1, c5_1, c8_2, c2_1, c10_1, c14_1 ---------------------------------------- (173) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(and(cons(z0, z1), x1)) -> c8(MARK(cons(z0, z1))) by MARK(and(cons(cons(y0, y1), z1), z2)) -> c8(MARK(cons(cons(y0, y1), z1))) MARK(and(cons(s(y0), z1), z2)) -> c8(MARK(cons(s(y0), z1))) MARK(and(cons(and(cons(y0, y1), y2), z1), z2)) -> c8(MARK(cons(and(cons(y0, y1), y2), z1))) MARK(and(cons(and(tt, y0), z1), z2)) -> c8(MARK(cons(and(tt, y0), z1))) MARK(and(cons(and(s(y0), y1), z1), z2)) -> c8(MARK(cons(and(s(y0), y1), z1))) MARK(and(cons(length(cons(y0, y1)), z1), z2)) -> c8(MARK(cons(length(cons(y0, y1)), z1))) MARK(and(cons(length(s(y0)), z1), z2)) -> c8(MARK(cons(length(s(y0)), z1))) MARK(and(cons(and(and(and(y0, y1), y2), y3), z1), z2)) -> c8(MARK(cons(and(and(and(y0, y1), y2), y3), z1))) MARK(and(cons(and(and(length(y0), y1), y2), z1), z2)) -> c8(MARK(cons(and(and(length(y0), y1), y2), z1))) MARK(and(cons(and(and(cons(y0, y1), y2), y3), z1), z2)) -> c8(MARK(cons(and(and(cons(y0, y1), y2), y3), z1))) MARK(and(cons(and(and(tt, y0), y1), z1), z2)) -> c8(MARK(cons(and(and(tt, y0), y1), z1))) MARK(and(cons(and(and(s(y0), y1), y2), z1), z2)) -> c8(MARK(cons(and(and(s(y0), y1), y2), z1))) MARK(and(cons(and(and(y0, y1), y2), z1), z2)) -> c8(MARK(cons(and(and(y0, y1), y2), z1))) MARK(and(cons(and(length(zeros), y0), z1), z2)) -> c8(MARK(cons(and(length(zeros), y0), z1))) MARK(and(cons(and(length(and(y0, y1)), y2), z1), z2)) -> c8(MARK(cons(and(length(and(y0, y1)), y2), z1))) MARK(and(cons(and(length(length(y0)), y1), z1), z2)) -> c8(MARK(cons(and(length(length(y0)), y1), z1))) MARK(and(cons(and(length(cons(y0, y1)), y2), z1), z2)) -> c8(MARK(cons(and(length(cons(y0, y1)), y2), z1))) MARK(and(cons(and(length(s(y0)), y1), z1), z2)) -> c8(MARK(cons(and(length(s(y0)), y1), z1))) MARK(and(cons(and(length(y0), y1), z1), z2)) -> c8(MARK(cons(and(length(y0), y1), z1))) MARK(and(cons(and(and(zeros, y0), y1), z1), z2)) -> c8(MARK(cons(and(and(zeros, y0), y1), z1))) MARK(and(cons(length(and(and(y0, y1), y2)), z1), z2)) -> c8(MARK(cons(length(and(and(y0, y1), y2)), z1))) MARK(and(cons(length(and(length(y0), y1)), z1), z2)) -> c8(MARK(cons(length(and(length(y0), y1)), z1))) MARK(and(cons(length(and(cons(y0, y1), y2)), z1), z2)) -> c8(MARK(cons(length(and(cons(y0, y1), y2)), z1))) MARK(and(cons(length(and(tt, y0)), z1), z2)) -> c8(MARK(cons(length(and(tt, y0)), z1))) MARK(and(cons(length(and(s(y0), y1)), z1), z2)) -> c8(MARK(cons(length(and(s(y0), y1)), z1))) MARK(and(cons(length(and(y0, y1)), z1), z2)) -> c8(MARK(cons(length(and(y0, y1)), z1))) MARK(and(cons(length(and(zeros, y0)), z1), z2)) -> c8(MARK(cons(length(and(zeros, y0)), z1))) MARK(and(cons(length(length(zeros)), z1), z2)) -> c8(MARK(cons(length(length(zeros)), z1))) MARK(and(cons(length(length(and(y0, y1))), z1), z2)) -> c8(MARK(cons(length(length(and(y0, y1))), z1))) MARK(and(cons(length(length(length(y0))), z1), z2)) -> c8(MARK(cons(length(length(length(y0))), z1))) MARK(and(cons(length(length(cons(y0, y1))), z1), z2)) -> c8(MARK(cons(length(length(cons(y0, y1))), z1))) MARK(and(cons(length(length(s(y0))), z1), z2)) -> c8(MARK(cons(length(length(s(y0))), z1))) MARK(and(cons(length(length(y0)), z1), z2)) -> c8(MARK(cons(length(length(y0)), z1))) MARK(and(cons(length(zeros), z1), z2)) -> c8(MARK(cons(length(zeros), z1))) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) MARK(cons(and(and(cons(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(cons(y0, y1), y2), y3))) MARK(cons(and(and(tt, y0), y1), z1)) -> c10(MARK(and(and(tt, y0), y1))) MARK(cons(and(and(s(y0), y1), y2), z1)) -> c10(MARK(and(and(s(y0), y1), y2))) MARK(cons(and(and(y0, y1), y2), z1)) -> c10(MARK(and(and(y0, y1), y2))) MARK(cons(and(length(zeros), y0), z1)) -> c10(MARK(and(length(zeros), y0))) MARK(cons(and(length(and(y0, y1)), y2), z1)) -> c10(MARK(and(length(and(y0, y1)), y2))) MARK(cons(and(length(length(y0)), y1), z1)) -> c10(MARK(and(length(length(y0)), y1))) MARK(cons(and(length(cons(y0, y1)), y2), z1)) -> c10(MARK(and(length(cons(y0, y1)), y2))) MARK(cons(and(length(s(y0)), y1), z1)) -> c10(MARK(and(length(s(y0)), y1))) MARK(cons(and(length(y0), y1), z1)) -> c10(MARK(and(length(y0), y1))) MARK(cons(and(and(zeros, y0), y1), z1)) -> c10(MARK(and(and(zeros, y0), y1))) MARK(cons(length(and(and(y0, y1), y2)), z1)) -> c10(MARK(length(and(and(y0, y1), y2)))) MARK(cons(length(and(length(y0), y1)), z1)) -> c10(MARK(length(and(length(y0), y1)))) MARK(cons(length(and(cons(y0, y1), y2)), z1)) -> c10(MARK(length(and(cons(y0, y1), y2)))) MARK(cons(length(and(tt, y0)), z1)) -> c10(MARK(length(and(tt, y0)))) MARK(cons(length(and(s(y0), y1)), z1)) -> c10(MARK(length(and(s(y0), y1)))) MARK(cons(length(and(y0, y1)), z1)) -> c10(MARK(length(and(y0, y1)))) MARK(cons(length(and(zeros, y0)), z1)) -> c10(MARK(length(and(zeros, y0)))) MARK(cons(length(length(zeros)), z1)) -> c10(MARK(length(length(zeros)))) MARK(cons(length(length(and(y0, y1))), z1)) -> c10(MARK(length(length(and(y0, y1))))) MARK(cons(length(length(length(y0))), z1)) -> c10(MARK(length(length(length(y0))))) MARK(cons(length(length(cons(y0, y1))), z1)) -> c10(MARK(length(length(cons(y0, y1))))) MARK(cons(length(length(s(y0))), z1)) -> c10(MARK(length(length(s(y0))))) MARK(cons(length(length(y0)), z1)) -> c10(MARK(length(length(y0)))) MARK(cons(length(zeros), z1)) -> c10(MARK(length(zeros))) MARK(s(s(y0))) -> c14(MARK(s(y0))) MARK(s(and(cons(y0, y1), y2))) -> c14(MARK(and(cons(y0, y1), y2))) MARK(s(and(tt, y0))) -> c14(MARK(and(tt, y0))) MARK(s(and(s(y0), y1))) -> c14(MARK(and(s(y0), y1))) MARK(s(length(cons(y0, y1)))) -> c14(MARK(length(cons(y0, y1)))) MARK(s(length(s(y0)))) -> c14(MARK(length(s(y0)))) MARK(s(and(and(and(y0, y1), y2), y3))) -> c14(MARK(and(and(and(y0, y1), y2), y3))) MARK(s(and(and(length(y0), y1), y2))) -> c14(MARK(and(and(length(y0), y1), y2))) MARK(s(and(and(cons(y0, 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c14(MARK(length(and(cons(y0, y1), y2)))) MARK(s(length(and(tt, y0)))) -> c14(MARK(length(and(tt, y0)))) MARK(s(length(and(s(y0), y1)))) -> c14(MARK(length(and(s(y0), y1)))) MARK(s(length(and(y0, y1)))) -> c14(MARK(length(and(y0, y1)))) MARK(s(length(and(zeros, y0)))) -> c14(MARK(length(and(zeros, y0)))) MARK(s(length(length(zeros)))) -> c14(MARK(length(length(zeros)))) MARK(s(length(length(and(y0, y1))))) -> c14(MARK(length(length(and(y0, y1))))) MARK(s(length(length(length(y0))))) -> c14(MARK(length(length(length(y0))))) MARK(s(length(length(cons(y0, y1))))) -> c14(MARK(length(length(cons(y0, y1))))) MARK(s(length(length(s(y0))))) -> c14(MARK(length(length(s(y0))))) MARK(s(length(length(y0)))) -> c14(MARK(length(length(y0)))) MARK(s(length(zeros))) -> c14(MARK(length(zeros))) MARK(s(cons(cons(y0, y1), y2))) -> c14(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c14(MARK(cons(s(y0), y1))) MARK(s(cons(and(cons(y0, y1), y2), y3))) -> c14(MARK(cons(and(cons(y0, y1), y2), y3))) MARK(s(cons(and(tt, y0), y1))) -> c14(MARK(cons(and(tt, y0), y1))) MARK(s(cons(and(s(y0), y1), y2))) -> c14(MARK(cons(and(s(y0), y1), y2))) MARK(s(cons(length(cons(y0, y1)), y2))) -> c14(MARK(cons(length(cons(y0, y1)), y2))) MARK(s(cons(length(s(y0)), y1))) -> c14(MARK(cons(length(s(y0)), y1))) MARK(s(cons(and(and(and(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(and(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(length(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(length(y0), y1), y2), y3))) MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(cons(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(tt, y0), y1), y2))) -> c14(MARK(cons(and(and(tt, y0), y1), y2))) MARK(s(cons(and(and(s(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(s(y0), y1), y2), y3))) MARK(s(cons(and(and(y0, y1), y2), y3))) -> c14(MARK(cons(and(and(y0, y1), y2), y3))) MARK(s(cons(and(length(zeros), y0), y1))) -> c14(MARK(cons(and(length(zeros), y0), y1))) MARK(s(cons(and(length(and(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(and(y0, y1)), y2), y3))) MARK(s(cons(and(length(length(y0)), y1), y2))) -> c14(MARK(cons(and(length(length(y0)), y1), y2))) MARK(s(cons(and(length(cons(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(cons(y0, y1)), y2), y3))) MARK(s(cons(and(length(s(y0)), y1), y2))) -> c14(MARK(cons(and(length(s(y0)), y1), y2))) MARK(s(cons(and(length(y0), y1), y2))) -> c14(MARK(cons(and(length(y0), y1), y2))) MARK(s(cons(and(and(zeros, y0), y1), y2))) -> c14(MARK(cons(and(and(zeros, y0), y1), y2))) MARK(s(cons(length(and(and(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(and(y0, y1), y2)), y3))) MARK(s(cons(length(and(length(y0), y1)), y2))) -> c14(MARK(cons(length(and(length(y0), y1)), y2))) MARK(s(cons(length(and(cons(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(cons(y0, y1), y2)), y3))) MARK(s(cons(length(and(tt, y0)), y1))) -> c14(MARK(cons(length(and(tt, y0)), y1))) MARK(s(cons(length(and(s(y0), y1)), y2))) -> c14(MARK(cons(length(and(s(y0), y1)), y2))) MARK(s(cons(length(and(y0, y1)), y2))) -> c14(MARK(cons(length(and(y0, y1)), y2))) MARK(s(cons(length(and(zeros, y0)), y1))) -> c14(MARK(cons(length(and(zeros, y0)), y1))) MARK(s(cons(length(length(zeros)), y0))) -> c14(MARK(cons(length(length(zeros)), y0))) MARK(s(cons(length(length(and(y0, y1))), y2))) -> c14(MARK(cons(length(length(and(y0, y1))), y2))) MARK(s(cons(length(length(length(y0))), y1))) -> c14(MARK(cons(length(length(length(y0))), y1))) MARK(s(cons(length(length(cons(y0, y1))), y2))) -> c14(MARK(cons(length(length(cons(y0, y1))), y2))) MARK(s(cons(length(length(s(y0))), y1))) -> c14(MARK(cons(length(length(s(y0))), y1))) MARK(s(cons(length(length(y0)), y1))) -> c14(MARK(cons(length(length(y0)), y1))) MARK(s(cons(length(zeros), y0))) -> c14(MARK(cons(length(zeros), y0))) A__LENGTH(cons(z0, s(s(y0)))) -> c5(MARK(s(s(y0)))) A__LENGTH(cons(z0, s(and(cons(y0, y1), y2)))) -> c5(MARK(s(and(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(tt, y0)))) -> c5(MARK(s(and(tt, y0)))) A__LENGTH(cons(z0, s(and(s(y0), y1)))) -> c5(MARK(s(and(s(y0), y1)))) A__LENGTH(cons(z0, s(length(cons(y0, y1))))) -> c5(MARK(s(length(cons(y0, y1))))) A__LENGTH(cons(z0, s(length(s(y0))))) -> c5(MARK(s(length(s(y0))))) A__LENGTH(cons(z0, s(and(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(length(y0), y1), y2)))) -> c5(MARK(s(and(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(tt, y0), y1)))) -> c5(MARK(s(and(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(and(and(s(y0), y1), y2)))) -> c5(MARK(s(and(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(y0, y1), y2)))) -> c5(MARK(s(and(and(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(length(zeros), y0)))) -> c5(MARK(s(and(length(zeros), y0)))) A__LENGTH(cons(z0, s(and(length(and(y0, y1)), y2)))) -> c5(MARK(s(and(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(length(y0)), y1)))) -> c5(MARK(s(and(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(cons(y0, y1)), y2)))) -> c5(MARK(s(and(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(s(y0)), y1)))) -> c5(MARK(s(and(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(y0), y1)))) -> c5(MARK(s(and(length(y0), y1)))) A__LENGTH(cons(z0, s(and(and(zeros, y0), y1)))) -> c5(MARK(s(and(and(zeros, y0), y1)))) A__LENGTH(cons(z0, s(length(and(and(y0, y1), y2))))) -> c5(MARK(s(length(and(and(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(length(y0), y1))))) -> c5(MARK(s(length(and(length(y0), y1))))) A__LENGTH(cons(z0, s(length(and(cons(y0, y1), y2))))) -> c5(MARK(s(length(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(tt, y0))))) -> c5(MARK(s(length(and(tt, y0))))) A__LENGTH(cons(z0, s(length(and(s(y0), y1))))) -> c5(MARK(s(length(and(s(y0), y1))))) A__LENGTH(cons(z0, s(length(and(y0, y1))))) -> c5(MARK(s(length(and(y0, y1))))) A__LENGTH(cons(z0, s(length(and(zeros, y0))))) -> c5(MARK(s(length(and(zeros, y0))))) A__LENGTH(cons(z0, s(length(length(zeros))))) -> c5(MARK(s(length(length(zeros))))) A__LENGTH(cons(z0, s(length(length(and(y0, y1)))))) -> c5(MARK(s(length(length(and(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(length(y0)))))) -> c5(MARK(s(length(length(length(y0)))))) A__LENGTH(cons(z0, s(length(length(cons(y0, y1)))))) -> c5(MARK(s(length(length(cons(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(s(y0)))))) -> c5(MARK(s(length(length(s(y0)))))) A__LENGTH(cons(z0, s(length(length(y0))))) -> c5(MARK(s(length(length(y0))))) A__LENGTH(cons(z0, s(length(zeros)))) -> c5(MARK(s(length(zeros)))) A__LENGTH(cons(z0, s(cons(cons(y0, y1), y2)))) -> c5(MARK(s(cons(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(cons(s(y0), y1)))) -> c5(MARK(s(cons(s(y0), y1)))) A__LENGTH(cons(z0, s(cons(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(tt, y0), y1)))) -> c5(MARK(s(cons(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(cons(and(s(y0), y1), y2)))) -> c5(MARK(s(cons(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(length(cons(y0, y1)), y2)))) -> c5(MARK(s(cons(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(s(y0)), y1)))) -> c5(MARK(s(cons(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(cons(and(and(and(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(and(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(length(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(length(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(cons(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(tt, y0), y1), y2)))) -> c5(MARK(s(cons(and(and(tt, y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(and(s(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(s(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(zeros), 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s(cons(length(and(cons(y0, y1), y2)), y3)))) -> c5(MARK(s(cons(length(and(cons(y0, y1), y2)), y3)))) A__LENGTH(cons(z0, s(cons(length(and(tt, y0)), y1)))) -> c5(MARK(s(cons(length(and(tt, y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(and(s(y0), y1)), y2)))) -> c5(MARK(s(cons(length(and(s(y0), y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(y0, y1)), y2)))) -> c5(MARK(s(cons(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(zeros, y0)), y1)))) -> c5(MARK(s(cons(length(and(zeros, y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(length(zeros)), y0)))) -> c5(MARK(s(cons(length(length(zeros)), y0)))) A__LENGTH(cons(z0, s(cons(length(length(and(y0, y1))), y2)))) -> c5(MARK(s(cons(length(length(and(y0, y1))), y2)))) A__LENGTH(cons(z0, s(cons(length(length(length(y0))), y1)))) -> c5(MARK(s(cons(length(length(length(y0))), y1)))) A__LENGTH(cons(z0, s(cons(length(length(cons(y0, y1))), y2)))) -> c5(MARK(s(cons(length(length(cons(y0, y1))), y2)))) A__LENGTH(cons(z0, s(cons(length(length(s(y0))), y1)))) -> c5(MARK(s(cons(length(length(s(y0))), y1)))) A__LENGTH(cons(z0, s(cons(length(length(y0)), y1)))) -> c5(MARK(s(cons(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(zeros), y0)))) -> c5(MARK(s(cons(length(zeros), y0)))) MARK(and(cons(cons(y0, y1), z1), z2)) -> c8(MARK(cons(cons(y0, y1), z1))) MARK(and(cons(s(y0), z1), z2)) -> c8(MARK(cons(s(y0), z1))) MARK(and(cons(and(cons(y0, y1), y2), z1), z2)) -> c8(MARK(cons(and(cons(y0, y1), y2), z1))) MARK(and(cons(and(tt, y0), z1), z2)) -> c8(MARK(cons(and(tt, y0), z1))) MARK(and(cons(and(s(y0), y1), z1), z2)) -> c8(MARK(cons(and(s(y0), y1), z1))) MARK(and(cons(length(cons(y0, y1)), z1), z2)) -> c8(MARK(cons(length(cons(y0, y1)), z1))) MARK(and(cons(length(s(y0)), z1), z2)) -> c8(MARK(cons(length(s(y0)), z1))) MARK(and(cons(and(and(and(y0, y1), y2), y3), z1), z2)) -> c8(MARK(cons(and(and(and(y0, y1), y2), y3), z1))) MARK(and(cons(and(and(length(y0), y1), y2), z1), z2)) -> c8(MARK(cons(and(and(length(y0), y1), y2), z1))) MARK(and(cons(and(and(cons(y0, y1), y2), y3), z1), z2)) -> c8(MARK(cons(and(and(cons(y0, y1), y2), y3), z1))) MARK(and(cons(and(and(tt, y0), y1), z1), z2)) -> c8(MARK(cons(and(and(tt, y0), y1), z1))) MARK(and(cons(and(and(s(y0), y1), y2), z1), z2)) -> c8(MARK(cons(and(and(s(y0), y1), y2), z1))) MARK(and(cons(and(and(y0, y1), y2), z1), z2)) -> c8(MARK(cons(and(and(y0, y1), y2), z1))) MARK(and(cons(and(length(zeros), y0), z1), z2)) -> c8(MARK(cons(and(length(zeros), y0), z1))) MARK(and(cons(and(length(and(y0, y1)), y2), z1), z2)) -> c8(MARK(cons(and(length(and(y0, y1)), y2), z1))) MARK(and(cons(and(length(length(y0)), y1), z1), z2)) -> c8(MARK(cons(and(length(length(y0)), y1), z1))) MARK(and(cons(and(length(cons(y0, y1)), y2), z1), z2)) -> c8(MARK(cons(and(length(cons(y0, y1)), y2), z1))) MARK(and(cons(and(length(s(y0)), y1), z1), z2)) -> c8(MARK(cons(and(length(s(y0)), y1), z1))) MARK(and(cons(and(length(y0), y1), z1), z2)) -> c8(MARK(cons(and(length(y0), y1), z1))) MARK(and(cons(and(and(zeros, y0), y1), z1), z2)) -> c8(MARK(cons(and(and(zeros, y0), y1), z1))) MARK(and(cons(length(and(and(y0, y1), y2)), z1), z2)) -> c8(MARK(cons(length(and(and(y0, y1), y2)), z1))) MARK(and(cons(length(and(length(y0), y1)), z1), z2)) -> c8(MARK(cons(length(and(length(y0), y1)), z1))) MARK(and(cons(length(and(cons(y0, y1), y2)), z1), z2)) -> c8(MARK(cons(length(and(cons(y0, y1), y2)), z1))) MARK(and(cons(length(and(tt, y0)), z1), z2)) -> c8(MARK(cons(length(and(tt, y0)), z1))) MARK(and(cons(length(and(s(y0), y1)), z1), z2)) -> c8(MARK(cons(length(and(s(y0), y1)), z1))) MARK(and(cons(length(and(y0, y1)), z1), z2)) -> c8(MARK(cons(length(and(y0, y1)), z1))) MARK(and(cons(length(and(zeros, y0)), z1), z2)) -> c8(MARK(cons(length(and(zeros, y0)), z1))) MARK(and(cons(length(length(zeros)), z1), z2)) -> c8(MARK(cons(length(length(zeros)), z1))) MARK(and(cons(length(length(and(y0, y1))), z1), z2)) -> c8(MARK(cons(length(length(and(y0, y1))), z1))) MARK(and(cons(length(length(length(y0))), z1), z2)) -> c8(MARK(cons(length(length(length(y0))), z1))) MARK(and(cons(length(length(cons(y0, y1))), z1), z2)) -> c8(MARK(cons(length(length(cons(y0, y1))), z1))) MARK(and(cons(length(length(s(y0))), z1), z2)) -> c8(MARK(cons(length(length(s(y0))), z1))) MARK(and(cons(length(length(y0)), z1), z2)) -> c8(MARK(cons(length(length(y0)), z1))) MARK(and(cons(length(zeros), z1), z2)) -> c8(MARK(cons(length(zeros), z1))) S tuples: A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) MARK(cons(and(and(cons(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(cons(y0, y1), y2), y3))) MARK(cons(and(and(tt, y0), y1), z1)) -> c10(MARK(and(and(tt, y0), y1))) MARK(cons(and(and(s(y0), y1), y2), z1)) -> c10(MARK(and(and(s(y0), y1), y2))) MARK(cons(and(and(y0, y1), y2), z1)) -> c10(MARK(and(and(y0, y1), y2))) MARK(cons(and(length(zeros), y0), z1)) -> c10(MARK(and(length(zeros), y0))) MARK(cons(and(length(and(y0, y1)), y2), z1)) -> c10(MARK(and(length(and(y0, y1)), y2))) MARK(cons(and(length(length(y0)), y1), z1)) -> c10(MARK(and(length(length(y0)), y1))) MARK(cons(and(length(cons(y0, y1)), y2), z1)) -> c10(MARK(and(length(cons(y0, y1)), y2))) MARK(cons(and(length(s(y0)), y1), z1)) -> c10(MARK(and(length(s(y0)), y1))) MARK(cons(and(length(y0), y1), z1)) -> c10(MARK(and(length(y0), y1))) MARK(cons(and(and(zeros, y0), y1), z1)) -> c10(MARK(and(and(zeros, y0), y1))) MARK(cons(length(and(and(y0, y1), y2)), z1)) -> c10(MARK(length(and(and(y0, y1), y2)))) MARK(cons(length(and(length(y0), y1)), z1)) -> c10(MARK(length(and(length(y0), y1)))) MARK(cons(length(and(cons(y0, y1), y2)), z1)) -> c10(MARK(length(and(cons(y0, y1), y2)))) MARK(cons(length(and(tt, y0)), z1)) -> c10(MARK(length(and(tt, y0)))) MARK(cons(length(and(s(y0), y1)), z1)) -> c10(MARK(length(and(s(y0), y1)))) MARK(cons(length(and(y0, y1)), z1)) -> c10(MARK(length(and(y0, y1)))) MARK(cons(length(and(zeros, y0)), z1)) -> c10(MARK(length(and(zeros, y0)))) MARK(cons(length(length(zeros)), z1)) -> c10(MARK(length(length(zeros)))) MARK(cons(length(length(and(y0, y1))), z1)) -> c10(MARK(length(length(and(y0, y1))))) MARK(cons(length(length(length(y0))), z1)) -> c10(MARK(length(length(length(y0))))) MARK(cons(length(length(cons(y0, y1))), z1)) -> c10(MARK(length(length(cons(y0, y1))))) MARK(cons(length(length(s(y0))), z1)) -> c10(MARK(length(length(s(y0))))) MARK(cons(length(length(y0)), z1)) -> c10(MARK(length(length(y0)))) MARK(cons(length(zeros), z1)) -> c10(MARK(length(zeros))) MARK(s(s(y0))) -> c14(MARK(s(y0))) MARK(s(and(cons(y0, y1), y2))) -> c14(MARK(and(cons(y0, y1), y2))) MARK(s(and(tt, y0))) -> c14(MARK(and(tt, y0))) MARK(s(and(s(y0), y1))) -> c14(MARK(and(s(y0), y1))) MARK(s(length(cons(y0, y1)))) -> c14(MARK(length(cons(y0, y1)))) MARK(s(length(s(y0)))) -> c14(MARK(length(s(y0)))) MARK(s(and(and(and(y0, y1), y2), y3))) -> c14(MARK(and(and(and(y0, y1), y2), y3))) MARK(s(and(and(length(y0), y1), y2))) -> c14(MARK(and(and(length(y0), y1), y2))) MARK(s(and(and(cons(y0, y1), y2), y3))) -> c14(MARK(and(and(cons(y0, y1), y2), y3))) MARK(s(and(and(tt, y0), y1))) -> c14(MARK(and(and(tt, y0), y1))) MARK(s(and(and(s(y0), y1), y2))) -> c14(MARK(and(and(s(y0), y1), y2))) MARK(s(and(and(y0, y1), y2))) -> c14(MARK(and(and(y0, y1), y2))) MARK(s(and(length(zeros), y0))) -> c14(MARK(and(length(zeros), y0))) MARK(s(and(length(and(y0, y1)), y2))) -> c14(MARK(and(length(and(y0, y1)), y2))) MARK(s(and(length(length(y0)), y1))) -> c14(MARK(and(length(length(y0)), y1))) MARK(s(and(length(cons(y0, y1)), y2))) -> c14(MARK(and(length(cons(y0, y1)), y2))) MARK(s(and(length(s(y0)), y1))) -> c14(MARK(and(length(s(y0)), y1))) MARK(s(and(length(y0), y1))) -> c14(MARK(and(length(y0), y1))) MARK(s(and(and(zeros, y0), y1))) -> c14(MARK(and(and(zeros, y0), y1))) MARK(s(length(and(and(y0, y1), y2)))) -> c14(MARK(length(and(and(y0, y1), y2)))) MARK(s(length(and(length(y0), y1)))) -> c14(MARK(length(and(length(y0), y1)))) MARK(s(length(and(cons(y0, y1), y2)))) -> c14(MARK(length(and(cons(y0, y1), y2)))) MARK(s(length(and(tt, y0)))) -> c14(MARK(length(and(tt, y0)))) MARK(s(length(and(s(y0), y1)))) -> c14(MARK(length(and(s(y0), y1)))) MARK(s(length(and(y0, y1)))) -> c14(MARK(length(and(y0, y1)))) MARK(s(length(and(zeros, y0)))) -> c14(MARK(length(and(zeros, y0)))) MARK(s(length(length(zeros)))) -> c14(MARK(length(length(zeros)))) MARK(s(length(length(and(y0, y1))))) -> c14(MARK(length(length(and(y0, y1))))) MARK(s(length(length(length(y0))))) -> c14(MARK(length(length(length(y0))))) MARK(s(length(length(cons(y0, y1))))) -> c14(MARK(length(length(cons(y0, y1))))) MARK(s(length(length(s(y0))))) -> c14(MARK(length(length(s(y0))))) MARK(s(length(length(y0)))) -> c14(MARK(length(length(y0)))) MARK(s(length(zeros))) -> c14(MARK(length(zeros))) MARK(s(cons(cons(y0, y1), y2))) -> c14(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c14(MARK(cons(s(y0), y1))) MARK(s(cons(and(cons(y0, y1), y2), y3))) -> c14(MARK(cons(and(cons(y0, y1), y2), y3))) MARK(s(cons(and(tt, y0), y1))) -> c14(MARK(cons(and(tt, y0), y1))) MARK(s(cons(and(s(y0), y1), y2))) -> c14(MARK(cons(and(s(y0), y1), y2))) MARK(s(cons(length(cons(y0, y1)), y2))) -> c14(MARK(cons(length(cons(y0, y1)), y2))) MARK(s(cons(length(s(y0)), y1))) -> c14(MARK(cons(length(s(y0)), y1))) MARK(s(cons(and(and(and(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(and(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(length(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(length(y0), y1), y2), y3))) MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(cons(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(tt, y0), y1), y2))) -> c14(MARK(cons(and(and(tt, y0), y1), y2))) MARK(s(cons(and(and(s(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(s(y0), y1), y2), y3))) MARK(s(cons(and(and(y0, y1), y2), y3))) -> c14(MARK(cons(and(and(y0, y1), y2), y3))) MARK(s(cons(and(length(zeros), y0), y1))) -> c14(MARK(cons(and(length(zeros), y0), y1))) MARK(s(cons(and(length(and(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(and(y0, y1)), y2), y3))) MARK(s(cons(and(length(length(y0)), y1), y2))) -> c14(MARK(cons(and(length(length(y0)), y1), y2))) MARK(s(cons(and(length(cons(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(cons(y0, y1)), y2), y3))) MARK(s(cons(and(length(s(y0)), y1), y2))) -> c14(MARK(cons(and(length(s(y0)), y1), y2))) MARK(s(cons(and(length(y0), y1), y2))) -> c14(MARK(cons(and(length(y0), y1), y2))) MARK(s(cons(and(and(zeros, y0), y1), y2))) -> c14(MARK(cons(and(and(zeros, y0), y1), y2))) MARK(s(cons(length(and(and(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(and(y0, y1), y2)), y3))) MARK(s(cons(length(and(length(y0), y1)), y2))) -> c14(MARK(cons(length(and(length(y0), y1)), y2))) MARK(s(cons(length(and(cons(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(cons(y0, y1), y2)), y3))) MARK(s(cons(length(and(tt, y0)), y1))) -> c14(MARK(cons(length(and(tt, y0)), y1))) MARK(s(cons(length(and(s(y0), y1)), y2))) -> c14(MARK(cons(length(and(s(y0), y1)), y2))) MARK(s(cons(length(and(y0, y1)), y2))) -> c14(MARK(cons(length(and(y0, y1)), y2))) MARK(s(cons(length(and(zeros, y0)), y1))) -> c14(MARK(cons(length(and(zeros, y0)), y1))) MARK(s(cons(length(length(zeros)), y0))) -> c14(MARK(cons(length(length(zeros)), y0))) MARK(s(cons(length(length(and(y0, y1))), y2))) -> c14(MARK(cons(length(length(and(y0, y1))), y2))) MARK(s(cons(length(length(length(y0))), y1))) -> c14(MARK(cons(length(length(length(y0))), y1))) MARK(s(cons(length(length(cons(y0, y1))), y2))) -> c14(MARK(cons(length(length(cons(y0, y1))), y2))) MARK(s(cons(length(length(s(y0))), y1))) -> c14(MARK(cons(length(length(s(y0))), y1))) MARK(s(cons(length(length(y0)), y1))) -> c14(MARK(cons(length(length(y0)), y1))) MARK(s(cons(length(zeros), y0))) -> c14(MARK(cons(length(zeros), y0))) A__LENGTH(cons(z0, s(s(y0)))) -> c5(MARK(s(s(y0)))) A__LENGTH(cons(z0, s(and(cons(y0, y1), y2)))) -> c5(MARK(s(and(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(tt, y0)))) -> c5(MARK(s(and(tt, y0)))) A__LENGTH(cons(z0, s(and(s(y0), y1)))) -> c5(MARK(s(and(s(y0), y1)))) A__LENGTH(cons(z0, s(length(cons(y0, y1))))) -> c5(MARK(s(length(cons(y0, y1))))) A__LENGTH(cons(z0, s(length(s(y0))))) -> c5(MARK(s(length(s(y0))))) A__LENGTH(cons(z0, s(and(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(length(y0), y1), y2)))) -> c5(MARK(s(and(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(tt, y0), y1)))) -> c5(MARK(s(and(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(and(and(s(y0), y1), y2)))) -> c5(MARK(s(and(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(y0, y1), y2)))) -> c5(MARK(s(and(and(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(length(zeros), y0)))) -> c5(MARK(s(and(length(zeros), y0)))) A__LENGTH(cons(z0, s(and(length(and(y0, y1)), y2)))) -> c5(MARK(s(and(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(length(y0)), y1)))) -> c5(MARK(s(and(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(cons(y0, y1)), y2)))) -> c5(MARK(s(and(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(s(y0)), y1)))) -> c5(MARK(s(and(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(y0), y1)))) -> c5(MARK(s(and(length(y0), y1)))) A__LENGTH(cons(z0, s(and(and(zeros, y0), y1)))) -> c5(MARK(s(and(and(zeros, y0), y1)))) A__LENGTH(cons(z0, s(length(and(and(y0, y1), y2))))) -> c5(MARK(s(length(and(and(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(length(y0), y1))))) -> c5(MARK(s(length(and(length(y0), y1))))) A__LENGTH(cons(z0, s(length(and(cons(y0, y1), y2))))) -> c5(MARK(s(length(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(tt, y0))))) -> c5(MARK(s(length(and(tt, y0))))) A__LENGTH(cons(z0, s(length(and(s(y0), y1))))) -> c5(MARK(s(length(and(s(y0), y1))))) A__LENGTH(cons(z0, s(length(and(y0, y1))))) -> c5(MARK(s(length(and(y0, y1))))) A__LENGTH(cons(z0, s(length(and(zeros, y0))))) -> c5(MARK(s(length(and(zeros, y0))))) A__LENGTH(cons(z0, s(length(length(zeros))))) -> c5(MARK(s(length(length(zeros))))) A__LENGTH(cons(z0, s(length(length(and(y0, y1)))))) -> c5(MARK(s(length(length(and(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(length(y0)))))) -> c5(MARK(s(length(length(length(y0)))))) A__LENGTH(cons(z0, s(length(length(cons(y0, y1)))))) -> c5(MARK(s(length(length(cons(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(s(y0)))))) -> c5(MARK(s(length(length(s(y0)))))) A__LENGTH(cons(z0, s(length(length(y0))))) -> c5(MARK(s(length(length(y0))))) A__LENGTH(cons(z0, s(length(zeros)))) -> c5(MARK(s(length(zeros)))) A__LENGTH(cons(z0, s(cons(cons(y0, y1), y2)))) -> c5(MARK(s(cons(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(cons(s(y0), y1)))) -> c5(MARK(s(cons(s(y0), y1)))) A__LENGTH(cons(z0, s(cons(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(tt, y0), y1)))) -> c5(MARK(s(cons(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(cons(and(s(y0), y1), y2)))) -> c5(MARK(s(cons(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(length(cons(y0, y1)), y2)))) -> c5(MARK(s(cons(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(s(y0)), y1)))) -> c5(MARK(s(cons(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(cons(and(and(and(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(and(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(length(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(length(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(cons(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(tt, y0), y1), y2)))) -> c5(MARK(s(cons(and(and(tt, y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(and(s(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(s(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(zeros), y0), y1)))) -> c5(MARK(s(cons(and(length(zeros), y0), y1)))) A__LENGTH(cons(z0, s(cons(and(length(and(y0, y1)), y2), y3)))) -> c5(MARK(s(cons(and(length(and(y0, y1)), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(length(y0)), y1), y2)))) -> c5(MARK(s(cons(and(length(length(y0)), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(length(cons(y0, y1)), y2), y3)))) -> c5(MARK(s(cons(and(length(cons(y0, y1)), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(s(y0)), y1), y2)))) -> c5(MARK(s(cons(and(length(s(y0)), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(length(y0), y1), y2)))) -> c5(MARK(s(cons(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(and(zeros, y0), y1), y2)))) -> c5(MARK(s(cons(and(and(zeros, y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(length(and(and(y0, y1), y2)), y3)))) -> c5(MARK(s(cons(length(and(and(y0, y1), y2)), y3)))) A__LENGTH(cons(z0, s(cons(length(and(length(y0), y1)), y2)))) -> c5(MARK(s(cons(length(and(length(y0), y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(cons(y0, y1), y2)), y3)))) -> c5(MARK(s(cons(length(and(cons(y0, y1), y2)), y3)))) A__LENGTH(cons(z0, s(cons(length(and(tt, y0)), y1)))) -> c5(MARK(s(cons(length(and(tt, y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(and(s(y0), y1)), y2)))) -> c5(MARK(s(cons(length(and(s(y0), y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(y0, y1)), y2)))) -> c5(MARK(s(cons(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(zeros, y0)), y1)))) -> c5(MARK(s(cons(length(and(zeros, y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(length(zeros)), y0)))) -> c5(MARK(s(cons(length(length(zeros)), y0)))) A__LENGTH(cons(z0, s(cons(length(length(and(y0, y1))), y2)))) -> c5(MARK(s(cons(length(length(and(y0, y1))), y2)))) A__LENGTH(cons(z0, s(cons(length(length(length(y0))), y1)))) -> c5(MARK(s(cons(length(length(length(y0))), y1)))) A__LENGTH(cons(z0, s(cons(length(length(cons(y0, y1))), y2)))) -> c5(MARK(s(cons(length(length(cons(y0, y1))), y2)))) A__LENGTH(cons(z0, s(cons(length(length(s(y0))), y1)))) -> c5(MARK(s(cons(length(length(s(y0))), y1)))) A__LENGTH(cons(z0, s(cons(length(length(y0)), y1)))) -> c5(MARK(s(cons(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(zeros), y0)))) -> c5(MARK(s(cons(length(zeros), y0)))) MARK(and(cons(cons(y0, y1), z1), z2)) -> c8(MARK(cons(cons(y0, y1), z1))) MARK(and(cons(s(y0), z1), z2)) -> c8(MARK(cons(s(y0), z1))) MARK(and(cons(and(cons(y0, y1), y2), z1), z2)) -> c8(MARK(cons(and(cons(y0, y1), y2), z1))) MARK(and(cons(and(tt, y0), z1), z2)) -> c8(MARK(cons(and(tt, y0), z1))) MARK(and(cons(and(s(y0), y1), z1), z2)) -> c8(MARK(cons(and(s(y0), y1), z1))) MARK(and(cons(length(cons(y0, y1)), z1), z2)) -> c8(MARK(cons(length(cons(y0, y1)), z1))) MARK(and(cons(length(s(y0)), z1), z2)) -> c8(MARK(cons(length(s(y0)), z1))) MARK(and(cons(and(and(and(y0, y1), y2), y3), z1), z2)) -> c8(MARK(cons(and(and(and(y0, y1), y2), y3), z1))) MARK(and(cons(and(and(length(y0), y1), y2), z1), z2)) -> c8(MARK(cons(and(and(length(y0), y1), y2), z1))) MARK(and(cons(and(and(cons(y0, y1), y2), y3), z1), z2)) -> c8(MARK(cons(and(and(cons(y0, y1), y2), y3), z1))) MARK(and(cons(and(and(tt, y0), y1), z1), z2)) -> c8(MARK(cons(and(and(tt, y0), y1), z1))) MARK(and(cons(and(and(s(y0), y1), y2), z1), z2)) -> c8(MARK(cons(and(and(s(y0), y1), y2), z1))) MARK(and(cons(and(and(y0, y1), y2), z1), z2)) -> c8(MARK(cons(and(and(y0, y1), y2), z1))) MARK(and(cons(and(length(zeros), y0), z1), z2)) -> c8(MARK(cons(and(length(zeros), y0), z1))) MARK(and(cons(and(length(and(y0, y1)), y2), z1), z2)) -> c8(MARK(cons(and(length(and(y0, y1)), y2), z1))) MARK(and(cons(and(length(length(y0)), y1), z1), z2)) -> c8(MARK(cons(and(length(length(y0)), y1), z1))) MARK(and(cons(and(length(cons(y0, y1)), y2), z1), z2)) -> c8(MARK(cons(and(length(cons(y0, y1)), y2), z1))) MARK(and(cons(and(length(s(y0)), y1), z1), z2)) -> c8(MARK(cons(and(length(s(y0)), y1), z1))) MARK(and(cons(and(length(y0), y1), z1), z2)) -> c8(MARK(cons(and(length(y0), y1), z1))) MARK(and(cons(and(and(zeros, y0), y1), z1), z2)) -> c8(MARK(cons(and(and(zeros, y0), y1), z1))) MARK(and(cons(length(and(and(y0, y1), y2)), z1), z2)) -> c8(MARK(cons(length(and(and(y0, y1), y2)), z1))) MARK(and(cons(length(and(length(y0), y1)), z1), z2)) -> c8(MARK(cons(length(and(length(y0), y1)), z1))) MARK(and(cons(length(and(cons(y0, y1), y2)), z1), z2)) -> c8(MARK(cons(length(and(cons(y0, y1), y2)), z1))) MARK(and(cons(length(and(tt, y0)), z1), z2)) -> c8(MARK(cons(length(and(tt, y0)), z1))) MARK(and(cons(length(and(s(y0), y1)), z1), z2)) -> c8(MARK(cons(length(and(s(y0), y1)), z1))) MARK(and(cons(length(and(y0, y1)), z1), z2)) -> c8(MARK(cons(length(and(y0, y1)), z1))) MARK(and(cons(length(and(zeros, y0)), z1), z2)) -> c8(MARK(cons(length(and(zeros, y0)), z1))) MARK(and(cons(length(length(zeros)), z1), z2)) -> c8(MARK(cons(length(length(zeros)), z1))) MARK(and(cons(length(length(and(y0, y1))), z1), z2)) -> c8(MARK(cons(length(length(and(y0, y1))), z1))) MARK(and(cons(length(length(length(y0))), z1), z2)) -> c8(MARK(cons(length(length(length(y0))), z1))) MARK(and(cons(length(length(cons(y0, y1))), z1), z2)) -> c8(MARK(cons(length(length(cons(y0, y1))), z1))) MARK(and(cons(length(length(s(y0))), z1), z2)) -> c8(MARK(cons(length(length(s(y0))), z1))) MARK(and(cons(length(length(y0)), z1), z2)) -> c8(MARK(cons(length(length(y0)), z1))) MARK(and(cons(length(zeros), z1), z2)) -> c8(MARK(cons(length(zeros), z1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__LENGTH_1, MARK_1, A__AND_2 Compound Symbols: c5_2, c8_1, c9_2, c9_1, c5_1, c8_2, c2_1, c10_1, c14_1 ---------------------------------------- (175) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(and(tt, x1)) -> c8(A__AND(tt, x1)) by MARK(and(tt, cons(y0, y1))) -> c8(A__AND(tt, cons(y0, y1))) MARK(and(tt, s(y0))) -> c8(A__AND(tt, s(y0))) MARK(and(tt, and(cons(y0, y1), y2))) -> c8(A__AND(tt, and(cons(y0, y1), y2))) MARK(and(tt, and(tt, y0))) -> c8(A__AND(tt, and(tt, y0))) MARK(and(tt, and(s(y0), y1))) -> c8(A__AND(tt, and(s(y0), y1))) MARK(and(tt, length(cons(y0, y1)))) -> c8(A__AND(tt, length(cons(y0, y1)))) MARK(and(tt, length(s(y0)))) -> c8(A__AND(tt, length(s(y0)))) MARK(and(tt, and(and(and(y0, y1), y2), y3))) -> c8(A__AND(tt, and(and(and(y0, y1), y2), y3))) MARK(and(tt, and(and(length(y0), y1), y2))) -> c8(A__AND(tt, and(and(length(y0), y1), y2))) MARK(and(tt, and(and(cons(y0, y1), y2), y3))) -> c8(A__AND(tt, and(and(cons(y0, y1), y2), y3))) MARK(and(tt, and(and(tt, y0), y1))) -> c8(A__AND(tt, and(and(tt, y0), y1))) MARK(and(tt, and(and(s(y0), y1), y2))) -> c8(A__AND(tt, and(and(s(y0), y1), y2))) MARK(and(tt, and(and(y0, y1), y2))) -> c8(A__AND(tt, and(and(y0, y1), y2))) MARK(and(tt, and(length(zeros), y0))) -> c8(A__AND(tt, and(length(zeros), y0))) MARK(and(tt, and(length(and(y0, y1)), y2))) -> c8(A__AND(tt, and(length(and(y0, y1)), y2))) MARK(and(tt, and(length(length(y0)), y1))) -> c8(A__AND(tt, and(length(length(y0)), y1))) MARK(and(tt, and(length(cons(y0, y1)), y2))) -> c8(A__AND(tt, and(length(cons(y0, y1)), y2))) MARK(and(tt, and(length(s(y0)), y1))) -> c8(A__AND(tt, and(length(s(y0)), y1))) MARK(and(tt, and(length(y0), y1))) -> c8(A__AND(tt, and(length(y0), y1))) MARK(and(tt, and(and(zeros, y0), y1))) -> c8(A__AND(tt, and(and(zeros, y0), y1))) MARK(and(tt, length(and(and(y0, y1), y2)))) -> c8(A__AND(tt, length(and(and(y0, y1), y2)))) MARK(and(tt, length(and(length(y0), y1)))) -> c8(A__AND(tt, length(and(length(y0), y1)))) MARK(and(tt, length(and(cons(y0, y1), y2)))) -> c8(A__AND(tt, length(and(cons(y0, y1), y2)))) MARK(and(tt, length(and(tt, y0)))) -> c8(A__AND(tt, length(and(tt, y0)))) MARK(and(tt, length(and(s(y0), y1)))) -> c8(A__AND(tt, length(and(s(y0), y1)))) MARK(and(tt, length(and(y0, y1)))) -> c8(A__AND(tt, length(and(y0, y1)))) MARK(and(tt, length(and(zeros, y0)))) -> c8(A__AND(tt, length(and(zeros, y0)))) MARK(and(tt, length(length(zeros)))) -> c8(A__AND(tt, length(length(zeros)))) MARK(and(tt, length(length(and(y0, y1))))) -> c8(A__AND(tt, length(length(and(y0, y1))))) MARK(and(tt, length(length(length(y0))))) -> c8(A__AND(tt, length(length(length(y0))))) MARK(and(tt, length(length(cons(y0, y1))))) -> c8(A__AND(tt, length(length(cons(y0, y1))))) MARK(and(tt, length(length(s(y0))))) -> c8(A__AND(tt, length(length(s(y0))))) MARK(and(tt, length(length(y0)))) -> c8(A__AND(tt, length(length(y0)))) MARK(and(tt, length(zeros))) -> c8(A__AND(tt, length(zeros))) ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) MARK(cons(and(and(cons(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(cons(y0, y1), y2), y3))) MARK(cons(and(and(tt, y0), y1), z1)) -> c10(MARK(and(and(tt, y0), y1))) MARK(cons(and(and(s(y0), y1), y2), z1)) -> c10(MARK(and(and(s(y0), y1), y2))) MARK(cons(and(and(y0, y1), y2), z1)) -> c10(MARK(and(and(y0, y1), y2))) MARK(cons(and(length(zeros), y0), z1)) -> c10(MARK(and(length(zeros), y0))) MARK(cons(and(length(and(y0, y1)), y2), z1)) -> c10(MARK(and(length(and(y0, y1)), y2))) MARK(cons(and(length(length(y0)), y1), z1)) -> c10(MARK(and(length(length(y0)), y1))) MARK(cons(and(length(cons(y0, y1)), y2), z1)) -> c10(MARK(and(length(cons(y0, y1)), y2))) MARK(cons(and(length(s(y0)), y1), z1)) -> c10(MARK(and(length(s(y0)), y1))) MARK(cons(and(length(y0), y1), z1)) -> c10(MARK(and(length(y0), y1))) MARK(cons(and(and(zeros, y0), y1), z1)) -> c10(MARK(and(and(zeros, y0), y1))) MARK(cons(length(and(and(y0, y1), y2)), z1)) -> c10(MARK(length(and(and(y0, y1), y2)))) MARK(cons(length(and(length(y0), y1)), z1)) -> c10(MARK(length(and(length(y0), y1)))) MARK(cons(length(and(cons(y0, y1), y2)), z1)) -> c10(MARK(length(and(cons(y0, y1), y2)))) MARK(cons(length(and(tt, y0)), z1)) -> c10(MARK(length(and(tt, y0)))) MARK(cons(length(and(s(y0), y1)), z1)) -> c10(MARK(length(and(s(y0), y1)))) MARK(cons(length(and(y0, y1)), z1)) -> c10(MARK(length(and(y0, y1)))) MARK(cons(length(and(zeros, y0)), z1)) -> c10(MARK(length(and(zeros, y0)))) MARK(cons(length(length(zeros)), z1)) -> c10(MARK(length(length(zeros)))) MARK(cons(length(length(and(y0, y1))), z1)) -> c10(MARK(length(length(and(y0, y1))))) MARK(cons(length(length(length(y0))), z1)) -> c10(MARK(length(length(length(y0))))) MARK(cons(length(length(cons(y0, y1))), z1)) -> c10(MARK(length(length(cons(y0, y1))))) MARK(cons(length(length(s(y0))), z1)) -> c10(MARK(length(length(s(y0))))) MARK(cons(length(length(y0)), z1)) -> c10(MARK(length(length(y0)))) MARK(cons(length(zeros), z1)) -> c10(MARK(length(zeros))) MARK(s(s(y0))) -> c14(MARK(s(y0))) MARK(s(and(cons(y0, y1), y2))) -> c14(MARK(and(cons(y0, y1), y2))) MARK(s(and(tt, y0))) -> c14(MARK(and(tt, y0))) MARK(s(and(s(y0), y1))) -> c14(MARK(and(s(y0), y1))) MARK(s(length(cons(y0, y1)))) -> c14(MARK(length(cons(y0, y1)))) MARK(s(length(s(y0)))) -> c14(MARK(length(s(y0)))) MARK(s(and(and(and(y0, y1), y2), y3))) -> c14(MARK(and(and(and(y0, y1), y2), y3))) MARK(s(and(and(length(y0), y1), y2))) -> c14(MARK(and(and(length(y0), y1), y2))) MARK(s(and(and(cons(y0, y1), y2), y3))) -> c14(MARK(and(and(cons(y0, y1), y2), y3))) MARK(s(and(and(tt, y0), y1))) -> c14(MARK(and(and(tt, y0), y1))) MARK(s(and(and(s(y0), y1), y2))) -> c14(MARK(and(and(s(y0), y1), y2))) MARK(s(and(and(y0, y1), y2))) -> c14(MARK(and(and(y0, y1), y2))) MARK(s(and(length(zeros), y0))) -> c14(MARK(and(length(zeros), y0))) MARK(s(and(length(and(y0, y1)), y2))) -> c14(MARK(and(length(and(y0, y1)), y2))) MARK(s(and(length(length(y0)), y1))) -> c14(MARK(and(length(length(y0)), y1))) MARK(s(and(length(cons(y0, y1)), y2))) -> c14(MARK(and(length(cons(y0, y1)), y2))) MARK(s(and(length(s(y0)), y1))) -> c14(MARK(and(length(s(y0)), y1))) MARK(s(and(length(y0), y1))) -> c14(MARK(and(length(y0), y1))) MARK(s(and(and(zeros, y0), y1))) -> c14(MARK(and(and(zeros, y0), y1))) MARK(s(length(and(and(y0, y1), y2)))) -> c14(MARK(length(and(and(y0, y1), y2)))) MARK(s(length(and(length(y0), y1)))) -> c14(MARK(length(and(length(y0), y1)))) MARK(s(length(and(cons(y0, y1), y2)))) -> c14(MARK(length(and(cons(y0, y1), y2)))) MARK(s(length(and(tt, y0)))) -> c14(MARK(length(and(tt, y0)))) MARK(s(length(and(s(y0), y1)))) -> c14(MARK(length(and(s(y0), y1)))) MARK(s(length(and(y0, y1)))) -> c14(MARK(length(and(y0, y1)))) MARK(s(length(and(zeros, y0)))) -> c14(MARK(length(and(zeros, y0)))) MARK(s(length(length(zeros)))) -> c14(MARK(length(length(zeros)))) MARK(s(length(length(and(y0, y1))))) -> c14(MARK(length(length(and(y0, y1))))) MARK(s(length(length(length(y0))))) -> c14(MARK(length(length(length(y0))))) MARK(s(length(length(cons(y0, y1))))) -> c14(MARK(length(length(cons(y0, y1))))) MARK(s(length(length(s(y0))))) -> c14(MARK(length(length(s(y0))))) MARK(s(length(length(y0)))) -> c14(MARK(length(length(y0)))) MARK(s(length(zeros))) -> c14(MARK(length(zeros))) MARK(s(cons(cons(y0, y1), y2))) -> c14(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c14(MARK(cons(s(y0), y1))) MARK(s(cons(and(cons(y0, y1), y2), y3))) -> c14(MARK(cons(and(cons(y0, y1), y2), y3))) MARK(s(cons(and(tt, y0), y1))) -> c14(MARK(cons(and(tt, y0), y1))) MARK(s(cons(and(s(y0), y1), y2))) -> c14(MARK(cons(and(s(y0), y1), y2))) MARK(s(cons(length(cons(y0, y1)), 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MARK(s(cons(and(length(cons(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(cons(y0, y1)), y2), y3))) MARK(s(cons(and(length(s(y0)), y1), y2))) -> c14(MARK(cons(and(length(s(y0)), y1), y2))) MARK(s(cons(and(length(y0), y1), y2))) -> c14(MARK(cons(and(length(y0), y1), y2))) MARK(s(cons(and(and(zeros, y0), y1), y2))) -> c14(MARK(cons(and(and(zeros, y0), y1), y2))) MARK(s(cons(length(and(and(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(and(y0, y1), y2)), y3))) MARK(s(cons(length(and(length(y0), y1)), y2))) -> c14(MARK(cons(length(and(length(y0), y1)), y2))) MARK(s(cons(length(and(cons(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(cons(y0, y1), y2)), y3))) MARK(s(cons(length(and(tt, y0)), y1))) -> c14(MARK(cons(length(and(tt, y0)), y1))) MARK(s(cons(length(and(s(y0), y1)), y2))) -> c14(MARK(cons(length(and(s(y0), y1)), y2))) MARK(s(cons(length(and(y0, y1)), y2))) -> c14(MARK(cons(length(and(y0, y1)), y2))) MARK(s(cons(length(and(zeros, y0)), y1))) -> c14(MARK(cons(length(and(zeros, 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A__LENGTH(cons(z0, s(length(s(y0))))) -> c5(MARK(s(length(s(y0))))) A__LENGTH(cons(z0, s(and(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(length(y0), y1), y2)))) -> c5(MARK(s(and(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(tt, y0), y1)))) -> c5(MARK(s(and(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(and(and(s(y0), y1), y2)))) -> c5(MARK(s(and(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(y0, y1), y2)))) -> c5(MARK(s(and(and(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(length(zeros), y0)))) -> c5(MARK(s(and(length(zeros), y0)))) A__LENGTH(cons(z0, s(and(length(and(y0, y1)), y2)))) -> c5(MARK(s(and(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(length(y0)), y1)))) -> c5(MARK(s(and(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(cons(y0, y1)), y2)))) -> c5(MARK(s(and(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(s(y0)), y1)))) -> c5(MARK(s(and(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(y0), y1)))) -> c5(MARK(s(and(length(y0), y1)))) A__LENGTH(cons(z0, s(and(and(zeros, y0), y1)))) -> c5(MARK(s(and(and(zeros, y0), y1)))) A__LENGTH(cons(z0, s(length(and(and(y0, y1), y2))))) -> c5(MARK(s(length(and(and(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(length(y0), y1))))) -> c5(MARK(s(length(and(length(y0), y1))))) A__LENGTH(cons(z0, s(length(and(cons(y0, y1), y2))))) -> c5(MARK(s(length(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(tt, y0))))) -> c5(MARK(s(length(and(tt, y0))))) A__LENGTH(cons(z0, s(length(and(s(y0), y1))))) -> c5(MARK(s(length(and(s(y0), y1))))) A__LENGTH(cons(z0, s(length(and(y0, y1))))) -> c5(MARK(s(length(and(y0, y1))))) A__LENGTH(cons(z0, s(length(and(zeros, y0))))) -> c5(MARK(s(length(and(zeros, y0))))) A__LENGTH(cons(z0, s(length(length(zeros))))) -> c5(MARK(s(length(length(zeros))))) A__LENGTH(cons(z0, s(length(length(and(y0, y1)))))) -> c5(MARK(s(length(length(and(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(length(y0)))))) -> c5(MARK(s(length(length(length(y0)))))) A__LENGTH(cons(z0, s(length(length(cons(y0, y1)))))) -> c5(MARK(s(length(length(cons(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(s(y0)))))) -> c5(MARK(s(length(length(s(y0)))))) A__LENGTH(cons(z0, s(length(length(y0))))) -> c5(MARK(s(length(length(y0))))) A__LENGTH(cons(z0, s(length(zeros)))) -> c5(MARK(s(length(zeros)))) A__LENGTH(cons(z0, s(cons(cons(y0, y1), y2)))) -> c5(MARK(s(cons(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(cons(s(y0), y1)))) -> c5(MARK(s(cons(s(y0), y1)))) A__LENGTH(cons(z0, s(cons(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(tt, y0), y1)))) -> c5(MARK(s(cons(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(cons(and(s(y0), y1), y2)))) -> c5(MARK(s(cons(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(length(cons(y0, y1)), y2)))) -> c5(MARK(s(cons(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(s(y0)), y1)))) -> c5(MARK(s(cons(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(cons(and(and(and(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(and(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(length(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(length(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(cons(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(tt, y0), y1), y2)))) -> c5(MARK(s(cons(and(and(tt, y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(and(s(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(s(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(zeros), y0), y1)))) -> c5(MARK(s(cons(and(length(zeros), y0), y1)))) A__LENGTH(cons(z0, s(cons(and(length(and(y0, y1)), y2), y3)))) -> c5(MARK(s(cons(and(length(and(y0, y1)), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(length(y0)), y1), y2)))) -> c5(MARK(s(cons(and(length(length(y0)), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(length(cons(y0, y1)), y2), y3)))) -> c5(MARK(s(cons(and(length(cons(y0, y1)), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(s(y0)), y1), y2)))) -> c5(MARK(s(cons(and(length(s(y0)), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(length(y0), y1), y2)))) -> c5(MARK(s(cons(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(and(zeros, y0), y1), y2)))) -> c5(MARK(s(cons(and(and(zeros, y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(length(and(and(y0, y1), y2)), y3)))) -> c5(MARK(s(cons(length(and(and(y0, y1), y2)), y3)))) A__LENGTH(cons(z0, s(cons(length(and(length(y0), y1)), y2)))) -> c5(MARK(s(cons(length(and(length(y0), y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(cons(y0, y1), y2)), y3)))) -> c5(MARK(s(cons(length(and(cons(y0, y1), y2)), y3)))) A__LENGTH(cons(z0, s(cons(length(and(tt, y0)), y1)))) -> c5(MARK(s(cons(length(and(tt, y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(and(s(y0), y1)), y2)))) -> c5(MARK(s(cons(length(and(s(y0), y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(y0, y1)), y2)))) -> c5(MARK(s(cons(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(zeros, y0)), y1)))) -> c5(MARK(s(cons(length(and(zeros, y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(length(zeros)), y0)))) -> c5(MARK(s(cons(length(length(zeros)), y0)))) A__LENGTH(cons(z0, s(cons(length(length(and(y0, y1))), y2)))) -> c5(MARK(s(cons(length(length(and(y0, y1))), y2)))) A__LENGTH(cons(z0, s(cons(length(length(length(y0))), y1)))) -> c5(MARK(s(cons(length(length(length(y0))), y1)))) A__LENGTH(cons(z0, s(cons(length(length(cons(y0, y1))), y2)))) -> c5(MARK(s(cons(length(length(cons(y0, y1))), y2)))) A__LENGTH(cons(z0, s(cons(length(length(s(y0))), y1)))) -> c5(MARK(s(cons(length(length(s(y0))), y1)))) A__LENGTH(cons(z0, s(cons(length(length(y0)), y1)))) -> c5(MARK(s(cons(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(zeros), y0)))) -> c5(MARK(s(cons(length(zeros), y0)))) MARK(and(cons(cons(y0, y1), z1), z2)) -> c8(MARK(cons(cons(y0, y1), z1))) MARK(and(cons(s(y0), z1), z2)) -> c8(MARK(cons(s(y0), z1))) MARK(and(cons(and(cons(y0, y1), y2), z1), z2)) -> c8(MARK(cons(and(cons(y0, y1), y2), z1))) MARK(and(cons(and(tt, y0), z1), z2)) -> c8(MARK(cons(and(tt, y0), z1))) MARK(and(cons(and(s(y0), y1), z1), z2)) -> c8(MARK(cons(and(s(y0), y1), z1))) MARK(and(cons(length(cons(y0, y1)), z1), z2)) -> c8(MARK(cons(length(cons(y0, y1)), z1))) MARK(and(cons(length(s(y0)), z1), z2)) -> c8(MARK(cons(length(s(y0)), z1))) MARK(and(cons(and(and(and(y0, y1), y2), y3), z1), z2)) -> c8(MARK(cons(and(and(and(y0, y1), y2), y3), z1))) MARK(and(cons(and(and(length(y0), y1), y2), z1), z2)) -> c8(MARK(cons(and(and(length(y0), y1), y2), z1))) MARK(and(cons(and(and(cons(y0, y1), y2), y3), z1), z2)) -> c8(MARK(cons(and(and(cons(y0, y1), y2), y3), z1))) MARK(and(cons(and(and(tt, y0), y1), z1), z2)) -> c8(MARK(cons(and(and(tt, y0), y1), z1))) MARK(and(cons(and(and(s(y0), y1), y2), z1), z2)) -> c8(MARK(cons(and(and(s(y0), y1), y2), z1))) MARK(and(cons(and(and(y0, y1), y2), z1), z2)) -> c8(MARK(cons(and(and(y0, y1), y2), z1))) MARK(and(cons(and(length(zeros), y0), z1), z2)) -> c8(MARK(cons(and(length(zeros), y0), z1))) MARK(and(cons(and(length(and(y0, y1)), y2), z1), z2)) -> c8(MARK(cons(and(length(and(y0, y1)), y2), z1))) MARK(and(cons(and(length(length(y0)), y1), z1), z2)) -> c8(MARK(cons(and(length(length(y0)), y1), z1))) MARK(and(cons(and(length(cons(y0, y1)), y2), z1), z2)) -> c8(MARK(cons(and(length(cons(y0, y1)), y2), z1))) MARK(and(cons(and(length(s(y0)), y1), z1), z2)) -> c8(MARK(cons(and(length(s(y0)), y1), z1))) MARK(and(cons(and(length(y0), y1), z1), z2)) -> c8(MARK(cons(and(length(y0), y1), z1))) MARK(and(cons(and(and(zeros, y0), y1), z1), z2)) -> c8(MARK(cons(and(and(zeros, y0), y1), z1))) MARK(and(cons(length(and(and(y0, y1), y2)), z1), z2)) -> c8(MARK(cons(length(and(and(y0, y1), y2)), z1))) MARK(and(cons(length(and(length(y0), y1)), z1), z2)) -> c8(MARK(cons(length(and(length(y0), y1)), z1))) MARK(and(cons(length(and(cons(y0, y1), y2)), z1), z2)) -> c8(MARK(cons(length(and(cons(y0, y1), y2)), z1))) MARK(and(cons(length(and(tt, y0)), z1), z2)) -> c8(MARK(cons(length(and(tt, y0)), z1))) MARK(and(cons(length(and(s(y0), y1)), z1), z2)) -> c8(MARK(cons(length(and(s(y0), y1)), z1))) MARK(and(cons(length(and(y0, y1)), z1), z2)) -> c8(MARK(cons(length(and(y0, y1)), z1))) MARK(and(cons(length(and(zeros, y0)), z1), z2)) -> c8(MARK(cons(length(and(zeros, y0)), z1))) MARK(and(cons(length(length(zeros)), z1), z2)) -> c8(MARK(cons(length(length(zeros)), z1))) MARK(and(cons(length(length(and(y0, y1))), z1), z2)) -> c8(MARK(cons(length(length(and(y0, y1))), z1))) MARK(and(cons(length(length(length(y0))), z1), z2)) -> c8(MARK(cons(length(length(length(y0))), z1))) MARK(and(cons(length(length(cons(y0, y1))), z1), z2)) -> c8(MARK(cons(length(length(cons(y0, y1))), z1))) MARK(and(cons(length(length(s(y0))), z1), z2)) -> c8(MARK(cons(length(length(s(y0))), z1))) MARK(and(cons(length(length(y0)), z1), z2)) -> c8(MARK(cons(length(length(y0)), z1))) MARK(and(cons(length(zeros), z1), z2)) -> c8(MARK(cons(length(zeros), z1))) MARK(and(tt, cons(y0, y1))) -> c8(A__AND(tt, cons(y0, y1))) MARK(and(tt, s(y0))) -> c8(A__AND(tt, s(y0))) MARK(and(tt, and(cons(y0, y1), y2))) -> c8(A__AND(tt, and(cons(y0, y1), y2))) MARK(and(tt, and(tt, y0))) -> c8(A__AND(tt, and(tt, y0))) MARK(and(tt, and(s(y0), y1))) -> c8(A__AND(tt, and(s(y0), y1))) MARK(and(tt, length(cons(y0, y1)))) -> c8(A__AND(tt, length(cons(y0, y1)))) MARK(and(tt, length(s(y0)))) -> c8(A__AND(tt, length(s(y0)))) MARK(and(tt, and(and(and(y0, y1), y2), y3))) -> c8(A__AND(tt, and(and(and(y0, y1), y2), y3))) MARK(and(tt, and(and(length(y0), y1), y2))) -> c8(A__AND(tt, and(and(length(y0), y1), y2))) MARK(and(tt, and(and(cons(y0, y1), y2), y3))) -> c8(A__AND(tt, and(and(cons(y0, y1), y2), y3))) MARK(and(tt, and(and(tt, y0), y1))) -> c8(A__AND(tt, and(and(tt, y0), y1))) MARK(and(tt, and(and(s(y0), y1), y2))) -> c8(A__AND(tt, and(and(s(y0), y1), y2))) MARK(and(tt, and(and(y0, y1), y2))) -> c8(A__AND(tt, and(and(y0, y1), y2))) MARK(and(tt, and(length(zeros), y0))) -> c8(A__AND(tt, and(length(zeros), y0))) MARK(and(tt, and(length(and(y0, y1)), y2))) -> c8(A__AND(tt, and(length(and(y0, y1)), y2))) MARK(and(tt, and(length(length(y0)), y1))) -> c8(A__AND(tt, and(length(length(y0)), y1))) MARK(and(tt, and(length(cons(y0, y1)), y2))) -> c8(A__AND(tt, and(length(cons(y0, y1)), y2))) MARK(and(tt, and(length(s(y0)), y1))) -> c8(A__AND(tt, and(length(s(y0)), y1))) MARK(and(tt, and(length(y0), y1))) -> c8(A__AND(tt, and(length(y0), y1))) MARK(and(tt, and(and(zeros, y0), y1))) -> c8(A__AND(tt, and(and(zeros, y0), y1))) MARK(and(tt, length(and(and(y0, y1), y2)))) -> c8(A__AND(tt, length(and(and(y0, y1), y2)))) MARK(and(tt, length(and(length(y0), y1)))) -> c8(A__AND(tt, length(and(length(y0), y1)))) MARK(and(tt, length(and(cons(y0, y1), y2)))) -> c8(A__AND(tt, length(and(cons(y0, y1), y2)))) MARK(and(tt, length(and(tt, y0)))) -> c8(A__AND(tt, length(and(tt, y0)))) MARK(and(tt, length(and(s(y0), y1)))) -> c8(A__AND(tt, length(and(s(y0), y1)))) MARK(and(tt, length(and(y0, y1)))) -> c8(A__AND(tt, length(and(y0, y1)))) MARK(and(tt, length(and(zeros, y0)))) -> c8(A__AND(tt, length(and(zeros, y0)))) MARK(and(tt, length(length(zeros)))) -> c8(A__AND(tt, length(length(zeros)))) MARK(and(tt, length(length(and(y0, y1))))) -> c8(A__AND(tt, length(length(and(y0, y1))))) MARK(and(tt, length(length(length(y0))))) -> c8(A__AND(tt, length(length(length(y0))))) MARK(and(tt, length(length(cons(y0, y1))))) -> c8(A__AND(tt, length(length(cons(y0, y1))))) MARK(and(tt, length(length(s(y0))))) -> c8(A__AND(tt, length(length(s(y0))))) MARK(and(tt, length(length(y0)))) -> c8(A__AND(tt, length(length(y0)))) MARK(and(tt, length(zeros))) -> c8(A__AND(tt, length(zeros))) S tuples: A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) MARK(cons(and(and(cons(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(cons(y0, y1), y2), y3))) MARK(cons(and(and(tt, y0), y1), z1)) -> c10(MARK(and(and(tt, y0), y1))) MARK(cons(and(and(s(y0), y1), y2), z1)) -> c10(MARK(and(and(s(y0), y1), y2))) MARK(cons(and(and(y0, y1), y2), z1)) -> c10(MARK(and(and(y0, y1), y2))) MARK(cons(and(length(zeros), y0), z1)) -> c10(MARK(and(length(zeros), y0))) MARK(cons(and(length(and(y0, y1)), y2), z1)) -> c10(MARK(and(length(and(y0, y1)), y2))) MARK(cons(and(length(length(y0)), y1), z1)) -> c10(MARK(and(length(length(y0)), y1))) MARK(cons(and(length(cons(y0, y1)), y2), z1)) -> c10(MARK(and(length(cons(y0, y1)), y2))) MARK(cons(and(length(s(y0)), y1), z1)) -> c10(MARK(and(length(s(y0)), y1))) MARK(cons(and(length(y0), y1), z1)) -> c10(MARK(and(length(y0), y1))) MARK(cons(and(and(zeros, y0), y1), z1)) -> c10(MARK(and(and(zeros, y0), y1))) MARK(cons(length(and(and(y0, y1), y2)), z1)) -> c10(MARK(length(and(and(y0, y1), y2)))) MARK(cons(length(and(length(y0), y1)), z1)) -> c10(MARK(length(and(length(y0), y1)))) MARK(cons(length(and(cons(y0, y1), y2)), z1)) -> c10(MARK(length(and(cons(y0, y1), y2)))) MARK(cons(length(and(tt, y0)), z1)) -> c10(MARK(length(and(tt, y0)))) MARK(cons(length(and(s(y0), y1)), z1)) -> c10(MARK(length(and(s(y0), y1)))) MARK(cons(length(and(y0, y1)), z1)) -> c10(MARK(length(and(y0, y1)))) MARK(cons(length(and(zeros, y0)), z1)) -> c10(MARK(length(and(zeros, y0)))) MARK(cons(length(length(zeros)), z1)) -> c10(MARK(length(length(zeros)))) MARK(cons(length(length(and(y0, y1))), z1)) -> c10(MARK(length(length(and(y0, y1))))) MARK(cons(length(length(length(y0))), z1)) -> c10(MARK(length(length(length(y0))))) MARK(cons(length(length(cons(y0, y1))), z1)) -> c10(MARK(length(length(cons(y0, y1))))) MARK(cons(length(length(s(y0))), z1)) -> c10(MARK(length(length(s(y0))))) MARK(cons(length(length(y0)), z1)) -> c10(MARK(length(length(y0)))) MARK(cons(length(zeros), z1)) -> c10(MARK(length(zeros))) MARK(s(s(y0))) -> c14(MARK(s(y0))) MARK(s(and(cons(y0, y1), y2))) -> c14(MARK(and(cons(y0, y1), y2))) MARK(s(and(tt, y0))) -> c14(MARK(and(tt, y0))) MARK(s(and(s(y0), y1))) -> c14(MARK(and(s(y0), y1))) MARK(s(length(cons(y0, y1)))) -> c14(MARK(length(cons(y0, y1)))) MARK(s(length(s(y0)))) -> c14(MARK(length(s(y0)))) MARK(s(and(and(and(y0, y1), y2), y3))) -> c14(MARK(and(and(and(y0, y1), y2), y3))) MARK(s(and(and(length(y0), y1), y2))) -> c14(MARK(and(and(length(y0), y1), y2))) MARK(s(and(and(cons(y0, y1), y2), y3))) -> c14(MARK(and(and(cons(y0, y1), y2), y3))) MARK(s(and(and(tt, y0), y1))) -> c14(MARK(and(and(tt, y0), y1))) MARK(s(and(and(s(y0), y1), y2))) -> c14(MARK(and(and(s(y0), y1), y2))) MARK(s(and(and(y0, y1), y2))) -> c14(MARK(and(and(y0, y1), y2))) MARK(s(and(length(zeros), y0))) -> c14(MARK(and(length(zeros), y0))) MARK(s(and(length(and(y0, y1)), y2))) -> c14(MARK(and(length(and(y0, y1)), y2))) MARK(s(and(length(length(y0)), y1))) -> c14(MARK(and(length(length(y0)), y1))) MARK(s(and(length(cons(y0, y1)), y2))) -> c14(MARK(and(length(cons(y0, y1)), y2))) MARK(s(and(length(s(y0)), y1))) -> c14(MARK(and(length(s(y0)), y1))) MARK(s(and(length(y0), y1))) -> c14(MARK(and(length(y0), y1))) MARK(s(and(and(zeros, y0), y1))) -> c14(MARK(and(and(zeros, y0), y1))) MARK(s(length(and(and(y0, y1), y2)))) -> c14(MARK(length(and(and(y0, y1), y2)))) MARK(s(length(and(length(y0), y1)))) -> c14(MARK(length(and(length(y0), y1)))) MARK(s(length(and(cons(y0, y1), y2)))) -> c14(MARK(length(and(cons(y0, y1), y2)))) MARK(s(length(and(tt, y0)))) -> c14(MARK(length(and(tt, y0)))) MARK(s(length(and(s(y0), y1)))) -> c14(MARK(length(and(s(y0), y1)))) MARK(s(length(and(y0, y1)))) -> c14(MARK(length(and(y0, y1)))) MARK(s(length(and(zeros, y0)))) -> c14(MARK(length(and(zeros, y0)))) MARK(s(length(length(zeros)))) -> c14(MARK(length(length(zeros)))) MARK(s(length(length(and(y0, y1))))) -> c14(MARK(length(length(and(y0, y1))))) MARK(s(length(length(length(y0))))) -> c14(MARK(length(length(length(y0))))) MARK(s(length(length(cons(y0, y1))))) -> c14(MARK(length(length(cons(y0, y1))))) MARK(s(length(length(s(y0))))) -> c14(MARK(length(length(s(y0))))) MARK(s(length(length(y0)))) -> c14(MARK(length(length(y0)))) MARK(s(length(zeros))) -> c14(MARK(length(zeros))) MARK(s(cons(cons(y0, y1), y2))) -> c14(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c14(MARK(cons(s(y0), y1))) MARK(s(cons(and(cons(y0, y1), y2), y3))) -> c14(MARK(cons(and(cons(y0, y1), y2), y3))) MARK(s(cons(and(tt, y0), y1))) -> c14(MARK(cons(and(tt, y0), y1))) MARK(s(cons(and(s(y0), y1), y2))) -> c14(MARK(cons(and(s(y0), y1), y2))) MARK(s(cons(length(cons(y0, y1)), y2))) -> c14(MARK(cons(length(cons(y0, y1)), y2))) MARK(s(cons(length(s(y0)), y1))) -> c14(MARK(cons(length(s(y0)), y1))) MARK(s(cons(and(and(and(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(and(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(length(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(length(y0), y1), y2), y3))) MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(cons(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(tt, y0), y1), y2))) -> c14(MARK(cons(and(and(tt, y0), y1), y2))) MARK(s(cons(and(and(s(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(s(y0), y1), y2), y3))) MARK(s(cons(and(and(y0, y1), y2), y3))) -> c14(MARK(cons(and(and(y0, y1), y2), y3))) MARK(s(cons(and(length(zeros), y0), y1))) -> c14(MARK(cons(and(length(zeros), y0), y1))) MARK(s(cons(and(length(and(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(and(y0, y1)), y2), y3))) MARK(s(cons(and(length(length(y0)), y1), y2))) -> c14(MARK(cons(and(length(length(y0)), y1), y2))) MARK(s(cons(and(length(cons(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(cons(y0, y1)), y2), y3))) MARK(s(cons(and(length(s(y0)), y1), y2))) -> c14(MARK(cons(and(length(s(y0)), y1), y2))) MARK(s(cons(and(length(y0), y1), y2))) -> c14(MARK(cons(and(length(y0), y1), y2))) MARK(s(cons(and(and(zeros, y0), y1), y2))) -> c14(MARK(cons(and(and(zeros, y0), y1), y2))) MARK(s(cons(length(and(and(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(and(y0, y1), y2)), y3))) MARK(s(cons(length(and(length(y0), y1)), y2))) -> c14(MARK(cons(length(and(length(y0), y1)), y2))) MARK(s(cons(length(and(cons(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(cons(y0, y1), y2)), y3))) MARK(s(cons(length(and(tt, y0)), y1))) -> c14(MARK(cons(length(and(tt, y0)), y1))) MARK(s(cons(length(and(s(y0), y1)), y2))) -> c14(MARK(cons(length(and(s(y0), y1)), y2))) MARK(s(cons(length(and(y0, y1)), y2))) -> c14(MARK(cons(length(and(y0, y1)), y2))) MARK(s(cons(length(and(zeros, y0)), y1))) -> c14(MARK(cons(length(and(zeros, y0)), y1))) MARK(s(cons(length(length(zeros)), y0))) -> c14(MARK(cons(length(length(zeros)), y0))) MARK(s(cons(length(length(and(y0, y1))), y2))) -> c14(MARK(cons(length(length(and(y0, y1))), y2))) MARK(s(cons(length(length(length(y0))), y1))) -> c14(MARK(cons(length(length(length(y0))), y1))) MARK(s(cons(length(length(cons(y0, y1))), y2))) -> c14(MARK(cons(length(length(cons(y0, y1))), y2))) MARK(s(cons(length(length(s(y0))), y1))) -> c14(MARK(cons(length(length(s(y0))), y1))) MARK(s(cons(length(length(y0)), y1))) -> c14(MARK(cons(length(length(y0)), y1))) MARK(s(cons(length(zeros), y0))) -> c14(MARK(cons(length(zeros), y0))) A__LENGTH(cons(z0, s(s(y0)))) -> c5(MARK(s(s(y0)))) A__LENGTH(cons(z0, s(and(cons(y0, y1), y2)))) -> c5(MARK(s(and(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(tt, y0)))) -> c5(MARK(s(and(tt, y0)))) A__LENGTH(cons(z0, s(and(s(y0), y1)))) -> c5(MARK(s(and(s(y0), y1)))) A__LENGTH(cons(z0, s(length(cons(y0, y1))))) -> c5(MARK(s(length(cons(y0, y1))))) A__LENGTH(cons(z0, s(length(s(y0))))) -> c5(MARK(s(length(s(y0))))) A__LENGTH(cons(z0, s(and(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(length(y0), y1), y2)))) -> c5(MARK(s(and(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(tt, y0), y1)))) -> c5(MARK(s(and(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(and(and(s(y0), y1), y2)))) -> c5(MARK(s(and(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(y0, y1), y2)))) -> c5(MARK(s(and(and(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(length(zeros), y0)))) -> c5(MARK(s(and(length(zeros), y0)))) A__LENGTH(cons(z0, s(and(length(and(y0, y1)), y2)))) -> c5(MARK(s(and(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(length(y0)), y1)))) -> c5(MARK(s(and(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(cons(y0, y1)), y2)))) -> c5(MARK(s(and(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(s(y0)), y1)))) -> c5(MARK(s(and(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(y0), y1)))) -> c5(MARK(s(and(length(y0), y1)))) A__LENGTH(cons(z0, s(and(and(zeros, y0), y1)))) -> c5(MARK(s(and(and(zeros, y0), y1)))) A__LENGTH(cons(z0, s(length(and(and(y0, y1), y2))))) -> c5(MARK(s(length(and(and(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(length(y0), y1))))) -> c5(MARK(s(length(and(length(y0), y1))))) A__LENGTH(cons(z0, s(length(and(cons(y0, y1), y2))))) -> c5(MARK(s(length(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(tt, y0))))) -> c5(MARK(s(length(and(tt, y0))))) A__LENGTH(cons(z0, s(length(and(s(y0), y1))))) -> c5(MARK(s(length(and(s(y0), y1))))) A__LENGTH(cons(z0, s(length(and(y0, y1))))) -> c5(MARK(s(length(and(y0, y1))))) A__LENGTH(cons(z0, s(length(and(zeros, y0))))) -> c5(MARK(s(length(and(zeros, y0))))) A__LENGTH(cons(z0, s(length(length(zeros))))) -> c5(MARK(s(length(length(zeros))))) A__LENGTH(cons(z0, s(length(length(and(y0, y1)))))) -> c5(MARK(s(length(length(and(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(length(y0)))))) -> c5(MARK(s(length(length(length(y0)))))) A__LENGTH(cons(z0, s(length(length(cons(y0, y1)))))) -> c5(MARK(s(length(length(cons(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(s(y0)))))) -> c5(MARK(s(length(length(s(y0)))))) A__LENGTH(cons(z0, s(length(length(y0))))) -> c5(MARK(s(length(length(y0))))) A__LENGTH(cons(z0, s(length(zeros)))) -> c5(MARK(s(length(zeros)))) A__LENGTH(cons(z0, s(cons(cons(y0, y1), y2)))) -> c5(MARK(s(cons(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(cons(s(y0), y1)))) -> c5(MARK(s(cons(s(y0), y1)))) A__LENGTH(cons(z0, s(cons(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(tt, y0), y1)))) -> c5(MARK(s(cons(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(cons(and(s(y0), y1), y2)))) -> c5(MARK(s(cons(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(length(cons(y0, y1)), y2)))) -> c5(MARK(s(cons(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(s(y0)), y1)))) -> c5(MARK(s(cons(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(cons(and(and(and(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(and(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(length(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(length(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(cons(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(tt, y0), y1), y2)))) -> c5(MARK(s(cons(and(and(tt, y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(and(s(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(s(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(zeros), y0), y1)))) -> c5(MARK(s(cons(and(length(zeros), y0), y1)))) A__LENGTH(cons(z0, s(cons(and(length(and(y0, y1)), y2), y3)))) -> c5(MARK(s(cons(and(length(and(y0, y1)), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(length(y0)), y1), y2)))) -> c5(MARK(s(cons(and(length(length(y0)), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(length(cons(y0, y1)), y2), y3)))) -> c5(MARK(s(cons(and(length(cons(y0, y1)), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(s(y0)), y1), y2)))) -> c5(MARK(s(cons(and(length(s(y0)), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(length(y0), y1), y2)))) -> c5(MARK(s(cons(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(and(zeros, y0), y1), y2)))) -> c5(MARK(s(cons(and(and(zeros, y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(length(and(and(y0, y1), y2)), y3)))) -> c5(MARK(s(cons(length(and(and(y0, y1), y2)), y3)))) A__LENGTH(cons(z0, s(cons(length(and(length(y0), y1)), y2)))) -> c5(MARK(s(cons(length(and(length(y0), y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(cons(y0, y1), y2)), y3)))) -> c5(MARK(s(cons(length(and(cons(y0, y1), y2)), y3)))) A__LENGTH(cons(z0, s(cons(length(and(tt, y0)), y1)))) -> c5(MARK(s(cons(length(and(tt, y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(and(s(y0), y1)), y2)))) -> c5(MARK(s(cons(length(and(s(y0), y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(y0, y1)), y2)))) -> c5(MARK(s(cons(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(zeros, y0)), y1)))) -> c5(MARK(s(cons(length(and(zeros, y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(length(zeros)), y0)))) -> c5(MARK(s(cons(length(length(zeros)), y0)))) A__LENGTH(cons(z0, s(cons(length(length(and(y0, y1))), y2)))) -> c5(MARK(s(cons(length(length(and(y0, y1))), y2)))) A__LENGTH(cons(z0, s(cons(length(length(length(y0))), y1)))) -> c5(MARK(s(cons(length(length(length(y0))), y1)))) A__LENGTH(cons(z0, s(cons(length(length(cons(y0, y1))), y2)))) -> c5(MARK(s(cons(length(length(cons(y0, y1))), y2)))) A__LENGTH(cons(z0, s(cons(length(length(s(y0))), y1)))) -> c5(MARK(s(cons(length(length(s(y0))), y1)))) A__LENGTH(cons(z0, s(cons(length(length(y0)), y1)))) -> c5(MARK(s(cons(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(zeros), y0)))) -> c5(MARK(s(cons(length(zeros), y0)))) MARK(and(cons(cons(y0, y1), z1), z2)) -> c8(MARK(cons(cons(y0, y1), z1))) MARK(and(cons(s(y0), z1), z2)) -> c8(MARK(cons(s(y0), z1))) MARK(and(cons(and(cons(y0, y1), y2), z1), z2)) -> c8(MARK(cons(and(cons(y0, y1), y2), z1))) MARK(and(cons(and(tt, y0), z1), z2)) -> c8(MARK(cons(and(tt, y0), z1))) MARK(and(cons(and(s(y0), y1), z1), z2)) -> c8(MARK(cons(and(s(y0), y1), z1))) MARK(and(cons(length(cons(y0, y1)), z1), z2)) -> c8(MARK(cons(length(cons(y0, y1)), z1))) MARK(and(cons(length(s(y0)), z1), z2)) -> c8(MARK(cons(length(s(y0)), z1))) MARK(and(cons(and(and(and(y0, y1), y2), y3), z1), z2)) -> c8(MARK(cons(and(and(and(y0, y1), y2), y3), z1))) MARK(and(cons(and(and(length(y0), y1), y2), z1), z2)) -> c8(MARK(cons(and(and(length(y0), y1), y2), z1))) MARK(and(cons(and(and(cons(y0, y1), y2), y3), z1), z2)) -> c8(MARK(cons(and(and(cons(y0, y1), y2), y3), z1))) MARK(and(cons(and(and(tt, y0), y1), z1), z2)) -> c8(MARK(cons(and(and(tt, y0), y1), z1))) MARK(and(cons(and(and(s(y0), y1), y2), z1), z2)) -> c8(MARK(cons(and(and(s(y0), y1), y2), z1))) MARK(and(cons(and(and(y0, y1), y2), z1), z2)) -> c8(MARK(cons(and(and(y0, y1), y2), z1))) MARK(and(cons(and(length(zeros), y0), z1), z2)) -> c8(MARK(cons(and(length(zeros), y0), z1))) MARK(and(cons(and(length(and(y0, y1)), y2), z1), z2)) -> c8(MARK(cons(and(length(and(y0, y1)), y2), z1))) MARK(and(cons(and(length(length(y0)), y1), z1), z2)) -> c8(MARK(cons(and(length(length(y0)), y1), z1))) MARK(and(cons(and(length(cons(y0, y1)), y2), z1), z2)) -> c8(MARK(cons(and(length(cons(y0, y1)), y2), z1))) MARK(and(cons(and(length(s(y0)), y1), z1), z2)) -> c8(MARK(cons(and(length(s(y0)), y1), z1))) MARK(and(cons(and(length(y0), y1), z1), z2)) -> c8(MARK(cons(and(length(y0), y1), z1))) MARK(and(cons(and(and(zeros, y0), y1), z1), z2)) -> c8(MARK(cons(and(and(zeros, y0), y1), z1))) MARK(and(cons(length(and(and(y0, y1), y2)), z1), z2)) -> c8(MARK(cons(length(and(and(y0, y1), y2)), z1))) MARK(and(cons(length(and(length(y0), y1)), z1), z2)) -> c8(MARK(cons(length(and(length(y0), y1)), z1))) MARK(and(cons(length(and(cons(y0, y1), y2)), z1), z2)) -> c8(MARK(cons(length(and(cons(y0, y1), y2)), z1))) MARK(and(cons(length(and(tt, y0)), z1), z2)) -> c8(MARK(cons(length(and(tt, y0)), z1))) MARK(and(cons(length(and(s(y0), y1)), z1), z2)) -> c8(MARK(cons(length(and(s(y0), y1)), z1))) MARK(and(cons(length(and(y0, y1)), z1), z2)) -> c8(MARK(cons(length(and(y0, y1)), z1))) MARK(and(cons(length(and(zeros, y0)), z1), z2)) -> c8(MARK(cons(length(and(zeros, y0)), z1))) MARK(and(cons(length(length(zeros)), z1), z2)) -> c8(MARK(cons(length(length(zeros)), z1))) MARK(and(cons(length(length(and(y0, y1))), z1), z2)) -> c8(MARK(cons(length(length(and(y0, y1))), z1))) MARK(and(cons(length(length(length(y0))), z1), z2)) -> c8(MARK(cons(length(length(length(y0))), z1))) MARK(and(cons(length(length(cons(y0, y1))), z1), z2)) -> c8(MARK(cons(length(length(cons(y0, y1))), z1))) MARK(and(cons(length(length(s(y0))), z1), z2)) -> c8(MARK(cons(length(length(s(y0))), z1))) MARK(and(cons(length(length(y0)), z1), z2)) -> c8(MARK(cons(length(length(y0)), z1))) MARK(and(cons(length(zeros), z1), z2)) -> c8(MARK(cons(length(zeros), z1))) MARK(and(tt, cons(y0, y1))) -> c8(A__AND(tt, cons(y0, y1))) MARK(and(tt, s(y0))) -> c8(A__AND(tt, s(y0))) MARK(and(tt, and(cons(y0, y1), y2))) -> c8(A__AND(tt, and(cons(y0, y1), y2))) MARK(and(tt, and(tt, y0))) -> c8(A__AND(tt, and(tt, y0))) MARK(and(tt, and(s(y0), y1))) -> c8(A__AND(tt, and(s(y0), y1))) MARK(and(tt, length(cons(y0, y1)))) -> c8(A__AND(tt, length(cons(y0, y1)))) MARK(and(tt, length(s(y0)))) -> c8(A__AND(tt, length(s(y0)))) MARK(and(tt, and(and(and(y0, y1), y2), y3))) -> c8(A__AND(tt, and(and(and(y0, y1), y2), y3))) MARK(and(tt, and(and(length(y0), y1), y2))) -> c8(A__AND(tt, and(and(length(y0), y1), y2))) MARK(and(tt, and(and(cons(y0, y1), y2), y3))) -> c8(A__AND(tt, and(and(cons(y0, y1), y2), y3))) MARK(and(tt, and(and(tt, y0), y1))) -> c8(A__AND(tt, and(and(tt, y0), y1))) MARK(and(tt, and(and(s(y0), y1), y2))) -> c8(A__AND(tt, and(and(s(y0), y1), y2))) MARK(and(tt, and(and(y0, y1), y2))) -> c8(A__AND(tt, and(and(y0, y1), y2))) MARK(and(tt, and(length(zeros), y0))) -> c8(A__AND(tt, and(length(zeros), y0))) MARK(and(tt, and(length(and(y0, y1)), y2))) -> c8(A__AND(tt, and(length(and(y0, y1)), y2))) MARK(and(tt, and(length(length(y0)), y1))) -> c8(A__AND(tt, and(length(length(y0)), y1))) MARK(and(tt, and(length(cons(y0, y1)), y2))) -> c8(A__AND(tt, and(length(cons(y0, y1)), y2))) MARK(and(tt, and(length(s(y0)), y1))) -> c8(A__AND(tt, and(length(s(y0)), y1))) MARK(and(tt, and(length(y0), y1))) -> c8(A__AND(tt, and(length(y0), y1))) MARK(and(tt, and(and(zeros, y0), y1))) -> c8(A__AND(tt, and(and(zeros, y0), y1))) MARK(and(tt, length(and(and(y0, y1), y2)))) -> c8(A__AND(tt, length(and(and(y0, y1), y2)))) MARK(and(tt, length(and(length(y0), y1)))) -> c8(A__AND(tt, length(and(length(y0), y1)))) MARK(and(tt, length(and(cons(y0, y1), y2)))) -> c8(A__AND(tt, length(and(cons(y0, y1), y2)))) MARK(and(tt, length(and(tt, y0)))) -> c8(A__AND(tt, length(and(tt, y0)))) MARK(and(tt, length(and(s(y0), y1)))) -> c8(A__AND(tt, length(and(s(y0), y1)))) MARK(and(tt, length(and(y0, y1)))) -> c8(A__AND(tt, length(and(y0, y1)))) MARK(and(tt, length(and(zeros, y0)))) -> c8(A__AND(tt, length(and(zeros, y0)))) MARK(and(tt, length(length(zeros)))) -> c8(A__AND(tt, length(length(zeros)))) MARK(and(tt, length(length(and(y0, y1))))) -> c8(A__AND(tt, length(length(and(y0, y1))))) MARK(and(tt, length(length(length(y0))))) -> c8(A__AND(tt, length(length(length(y0))))) MARK(and(tt, length(length(cons(y0, y1))))) -> c8(A__AND(tt, length(length(cons(y0, y1))))) MARK(and(tt, length(length(s(y0))))) -> c8(A__AND(tt, length(length(s(y0))))) MARK(and(tt, length(length(y0)))) -> c8(A__AND(tt, length(length(y0)))) MARK(and(tt, length(zeros))) -> c8(A__AND(tt, length(zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__LENGTH_1, MARK_1, A__AND_2 Compound Symbols: c5_2, c8_1, c9_2, c9_1, c5_1, c8_2, c2_1, c10_1, c14_1 ---------------------------------------- (177) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(and(s(z0), x1)) -> c8(MARK(s(z0))) by MARK(and(s(s(y0)), z1)) -> c8(MARK(s(s(y0)))) MARK(and(s(and(cons(y0, y1), y2)), z1)) -> c8(MARK(s(and(cons(y0, y1), y2)))) MARK(and(s(and(tt, y0)), z1)) -> c8(MARK(s(and(tt, y0)))) MARK(and(s(and(s(y0), y1)), z1)) -> c8(MARK(s(and(s(y0), y1)))) MARK(and(s(length(cons(y0, y1))), z1)) -> c8(MARK(s(length(cons(y0, y1))))) MARK(and(s(length(s(y0))), z1)) -> c8(MARK(s(length(s(y0))))) MARK(and(s(and(and(and(y0, y1), y2), y3)), z1)) -> c8(MARK(s(and(and(and(y0, y1), y2), y3)))) MARK(and(s(and(and(length(y0), y1), y2)), z1)) -> c8(MARK(s(and(and(length(y0), y1), y2)))) MARK(and(s(and(and(cons(y0, y1), y2), y3)), z1)) -> c8(MARK(s(and(and(cons(y0, y1), y2), y3)))) MARK(and(s(and(and(tt, y0), y1)), z1)) -> c8(MARK(s(and(and(tt, y0), y1)))) MARK(and(s(and(and(s(y0), y1), y2)), z1)) -> c8(MARK(s(and(and(s(y0), y1), y2)))) MARK(and(s(and(and(y0, y1), y2)), z1)) -> c8(MARK(s(and(and(y0, y1), y2)))) MARK(and(s(and(length(zeros), y0)), z1)) -> c8(MARK(s(and(length(zeros), y0)))) MARK(and(s(and(length(and(y0, y1)), y2)), z1)) -> c8(MARK(s(and(length(and(y0, y1)), y2)))) MARK(and(s(and(length(length(y0)), y1)), z1)) -> c8(MARK(s(and(length(length(y0)), y1)))) MARK(and(s(and(length(cons(y0, y1)), y2)), z1)) -> c8(MARK(s(and(length(cons(y0, y1)), y2)))) MARK(and(s(and(length(s(y0)), y1)), z1)) -> c8(MARK(s(and(length(s(y0)), y1)))) MARK(and(s(and(length(y0), y1)), z1)) -> c8(MARK(s(and(length(y0), y1)))) MARK(and(s(and(and(zeros, y0), y1)), z1)) -> c8(MARK(s(and(and(zeros, y0), y1)))) MARK(and(s(length(and(and(y0, y1), y2))), z1)) -> c8(MARK(s(length(and(and(y0, y1), y2))))) MARK(and(s(length(and(length(y0), y1))), z1)) -> c8(MARK(s(length(and(length(y0), y1))))) MARK(and(s(length(and(cons(y0, y1), y2))), z1)) -> c8(MARK(s(length(and(cons(y0, y1), y2))))) MARK(and(s(length(and(tt, y0))), z1)) -> c8(MARK(s(length(and(tt, y0))))) MARK(and(s(length(and(s(y0), y1))), z1)) -> c8(MARK(s(length(and(s(y0), y1))))) MARK(and(s(length(and(y0, y1))), z1)) -> c8(MARK(s(length(and(y0, y1))))) MARK(and(s(length(and(zeros, y0))), z1)) -> c8(MARK(s(length(and(zeros, y0))))) MARK(and(s(length(length(zeros))), z1)) -> c8(MARK(s(length(length(zeros))))) MARK(and(s(length(length(and(y0, y1)))), z1)) -> c8(MARK(s(length(length(and(y0, y1)))))) MARK(and(s(length(length(length(y0)))), z1)) -> c8(MARK(s(length(length(length(y0)))))) MARK(and(s(length(length(cons(y0, y1)))), z1)) -> c8(MARK(s(length(length(cons(y0, y1)))))) MARK(and(s(length(length(s(y0)))), z1)) -> c8(MARK(s(length(length(s(y0)))))) MARK(and(s(length(length(y0))), z1)) -> c8(MARK(s(length(length(y0))))) MARK(and(s(length(zeros)), z1)) -> c8(MARK(s(length(zeros)))) MARK(and(s(cons(cons(y0, y1), y2)), z1)) -> c8(MARK(s(cons(cons(y0, y1), y2)))) MARK(and(s(cons(s(y0), y1)), z1)) -> c8(MARK(s(cons(s(y0), y1)))) MARK(and(s(cons(and(cons(y0, y1), y2), y3)), z1)) -> c8(MARK(s(cons(and(cons(y0, y1), y2), y3)))) MARK(and(s(cons(and(tt, y0), y1)), z1)) -> c8(MARK(s(cons(and(tt, y0), y1)))) MARK(and(s(cons(and(s(y0), y1), y2)), z1)) -> c8(MARK(s(cons(and(s(y0), y1), y2)))) MARK(and(s(cons(length(cons(y0, y1)), y2)), z1)) -> c8(MARK(s(cons(length(cons(y0, y1)), y2)))) MARK(and(s(cons(length(s(y0)), y1)), z1)) -> c8(MARK(s(cons(length(s(y0)), y1)))) MARK(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), z1)) -> c8(MARK(s(cons(and(and(and(y0, y1), y2), y3), y4)))) MARK(and(s(cons(and(and(length(y0), y1), y2), y3)), z1)) -> c8(MARK(s(cons(and(and(length(y0), y1), y2), y3)))) MARK(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), z1)) -> c8(MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) MARK(and(s(cons(and(and(tt, y0), y1), y2)), z1)) -> c8(MARK(s(cons(and(and(tt, y0), y1), y2)))) MARK(and(s(cons(and(and(s(y0), y1), y2), y3)), z1)) -> c8(MARK(s(cons(and(and(s(y0), y1), y2), y3)))) MARK(and(s(cons(and(and(y0, y1), y2), y3)), z1)) -> c8(MARK(s(cons(and(and(y0, y1), y2), y3)))) MARK(and(s(cons(and(length(zeros), y0), y1)), z1)) -> c8(MARK(s(cons(and(length(zeros), y0), y1)))) MARK(and(s(cons(and(length(and(y0, y1)), y2), y3)), z1)) -> c8(MARK(s(cons(and(length(and(y0, y1)), y2), y3)))) MARK(and(s(cons(and(length(length(y0)), y1), y2)), z1)) -> c8(MARK(s(cons(and(length(length(y0)), y1), y2)))) MARK(and(s(cons(and(length(cons(y0, y1)), y2), y3)), z1)) -> c8(MARK(s(cons(and(length(cons(y0, y1)), y2), y3)))) MARK(and(s(cons(and(length(s(y0)), y1), y2)), z1)) -> c8(MARK(s(cons(and(length(s(y0)), y1), y2)))) MARK(and(s(cons(and(length(y0), y1), y2)), z1)) -> c8(MARK(s(cons(and(length(y0), y1), y2)))) MARK(and(s(cons(and(and(zeros, y0), y1), y2)), z1)) -> c8(MARK(s(cons(and(and(zeros, y0), y1), y2)))) MARK(and(s(cons(length(and(and(y0, y1), y2)), y3)), z1)) -> c8(MARK(s(cons(length(and(and(y0, y1), y2)), y3)))) MARK(and(s(cons(length(and(length(y0), y1)), y2)), z1)) -> c8(MARK(s(cons(length(and(length(y0), y1)), y2)))) MARK(and(s(cons(length(and(cons(y0, y1), y2)), y3)), z1)) -> c8(MARK(s(cons(length(and(cons(y0, y1), y2)), y3)))) MARK(and(s(cons(length(and(tt, y0)), y1)), z1)) -> c8(MARK(s(cons(length(and(tt, y0)), y1)))) MARK(and(s(cons(length(and(s(y0), y1)), y2)), z1)) -> c8(MARK(s(cons(length(and(s(y0), y1)), y2)))) MARK(and(s(cons(length(and(y0, y1)), y2)), z1)) -> c8(MARK(s(cons(length(and(y0, y1)), y2)))) MARK(and(s(cons(length(and(zeros, y0)), y1)), z1)) -> c8(MARK(s(cons(length(and(zeros, y0)), y1)))) MARK(and(s(cons(length(length(zeros)), y0)), z1)) -> c8(MARK(s(cons(length(length(zeros)), y0)))) MARK(and(s(cons(length(length(and(y0, y1))), y2)), z1)) -> c8(MARK(s(cons(length(length(and(y0, y1))), y2)))) MARK(and(s(cons(length(length(length(y0))), y1)), z1)) -> c8(MARK(s(cons(length(length(length(y0))), y1)))) MARK(and(s(cons(length(length(cons(y0, y1))), y2)), z1)) -> c8(MARK(s(cons(length(length(cons(y0, y1))), y2)))) MARK(and(s(cons(length(length(s(y0))), y1)), z1)) -> c8(MARK(s(cons(length(length(s(y0))), y1)))) MARK(and(s(cons(length(length(y0)), y1)), z1)) -> c8(MARK(s(cons(length(length(y0)), y1)))) MARK(and(s(cons(length(zeros), y0)), z1)) -> c8(MARK(s(cons(length(zeros), y0)))) ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) MARK(cons(and(and(cons(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(cons(y0, y1), y2), y3))) MARK(cons(and(and(tt, y0), y1), z1)) -> c10(MARK(and(and(tt, y0), y1))) MARK(cons(and(and(s(y0), y1), y2), z1)) -> c10(MARK(and(and(s(y0), y1), y2))) MARK(cons(and(and(y0, y1), y2), z1)) -> c10(MARK(and(and(y0, y1), y2))) MARK(cons(and(length(zeros), y0), z1)) -> c10(MARK(and(length(zeros), y0))) MARK(cons(and(length(and(y0, y1)), y2), z1)) -> c10(MARK(and(length(and(y0, y1)), y2))) MARK(cons(and(length(length(y0)), y1), z1)) -> c10(MARK(and(length(length(y0)), y1))) MARK(cons(and(length(cons(y0, y1)), y2), z1)) -> c10(MARK(and(length(cons(y0, y1)), y2))) MARK(cons(and(length(s(y0)), y1), z1)) -> c10(MARK(and(length(s(y0)), y1))) MARK(cons(and(length(y0), y1), z1)) -> c10(MARK(and(length(y0), y1))) MARK(cons(and(and(zeros, y0), y1), z1)) -> c10(MARK(and(and(zeros, y0), y1))) MARK(cons(length(and(and(y0, y1), y2)), z1)) -> c10(MARK(length(and(and(y0, y1), y2)))) MARK(cons(length(and(length(y0), y1)), z1)) -> c10(MARK(length(and(length(y0), y1)))) MARK(cons(length(and(cons(y0, y1), y2)), z1)) -> c10(MARK(length(and(cons(y0, y1), y2)))) MARK(cons(length(and(tt, y0)), z1)) -> c10(MARK(length(and(tt, y0)))) MARK(cons(length(and(s(y0), y1)), z1)) -> c10(MARK(length(and(s(y0), y1)))) MARK(cons(length(and(y0, y1)), z1)) -> c10(MARK(length(and(y0, y1)))) MARK(cons(length(and(zeros, y0)), z1)) -> c10(MARK(length(and(zeros, y0)))) MARK(cons(length(length(zeros)), z1)) -> c10(MARK(length(length(zeros)))) MARK(cons(length(length(and(y0, y1))), z1)) -> c10(MARK(length(length(and(y0, y1))))) MARK(cons(length(length(length(y0))), z1)) -> c10(MARK(length(length(length(y0))))) MARK(cons(length(length(cons(y0, y1))), z1)) -> c10(MARK(length(length(cons(y0, y1))))) MARK(cons(length(length(s(y0))), z1)) -> c10(MARK(length(length(s(y0))))) MARK(cons(length(length(y0)), z1)) -> c10(MARK(length(length(y0)))) MARK(cons(length(zeros), z1)) -> c10(MARK(length(zeros))) MARK(s(s(y0))) -> c14(MARK(s(y0))) MARK(s(and(cons(y0, y1), y2))) -> c14(MARK(and(cons(y0, y1), y2))) MARK(s(and(tt, y0))) -> c14(MARK(and(tt, y0))) MARK(s(and(s(y0), y1))) -> 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c14(MARK(cons(length(and(length(y0), y1)), y2))) MARK(s(cons(length(and(cons(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(cons(y0, y1), y2)), y3))) MARK(s(cons(length(and(tt, y0)), y1))) -> c14(MARK(cons(length(and(tt, y0)), y1))) MARK(s(cons(length(and(s(y0), y1)), y2))) -> c14(MARK(cons(length(and(s(y0), y1)), y2))) MARK(s(cons(length(and(y0, y1)), y2))) -> c14(MARK(cons(length(and(y0, y1)), y2))) MARK(s(cons(length(and(zeros, y0)), y1))) -> c14(MARK(cons(length(and(zeros, y0)), y1))) MARK(s(cons(length(length(zeros)), y0))) -> c14(MARK(cons(length(length(zeros)), y0))) MARK(s(cons(length(length(and(y0, y1))), y2))) -> c14(MARK(cons(length(length(and(y0, y1))), y2))) MARK(s(cons(length(length(length(y0))), y1))) -> c14(MARK(cons(length(length(length(y0))), y1))) MARK(s(cons(length(length(cons(y0, y1))), y2))) -> c14(MARK(cons(length(length(cons(y0, y1))), y2))) MARK(s(cons(length(length(s(y0))), y1))) -> c14(MARK(cons(length(length(s(y0))), y1))) MARK(s(cons(length(length(y0)), y1))) -> c14(MARK(cons(length(length(y0)), y1))) MARK(s(cons(length(zeros), y0))) -> c14(MARK(cons(length(zeros), y0))) A__LENGTH(cons(z0, s(s(y0)))) -> c5(MARK(s(s(y0)))) A__LENGTH(cons(z0, s(and(cons(y0, y1), y2)))) -> c5(MARK(s(and(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(tt, y0)))) -> c5(MARK(s(and(tt, y0)))) A__LENGTH(cons(z0, s(and(s(y0), y1)))) -> c5(MARK(s(and(s(y0), y1)))) A__LENGTH(cons(z0, s(length(cons(y0, y1))))) -> c5(MARK(s(length(cons(y0, y1))))) A__LENGTH(cons(z0, s(length(s(y0))))) -> c5(MARK(s(length(s(y0))))) A__LENGTH(cons(z0, s(and(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(length(y0), y1), y2)))) -> c5(MARK(s(and(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(tt, y0), y1)))) -> c5(MARK(s(and(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(and(and(s(y0), y1), y2)))) -> c5(MARK(s(and(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(y0, y1), y2)))) -> c5(MARK(s(and(and(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(length(zeros), y0)))) -> c5(MARK(s(and(length(zeros), y0)))) A__LENGTH(cons(z0, s(and(length(and(y0, y1)), y2)))) -> c5(MARK(s(and(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(length(y0)), y1)))) -> c5(MARK(s(and(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(cons(y0, y1)), y2)))) -> c5(MARK(s(and(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(s(y0)), y1)))) -> c5(MARK(s(and(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(y0), y1)))) -> c5(MARK(s(and(length(y0), y1)))) A__LENGTH(cons(z0, s(and(and(zeros, y0), y1)))) -> c5(MARK(s(and(and(zeros, y0), y1)))) A__LENGTH(cons(z0, s(length(and(and(y0, y1), y2))))) -> c5(MARK(s(length(and(and(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(length(y0), y1))))) -> c5(MARK(s(length(and(length(y0), y1))))) A__LENGTH(cons(z0, s(length(and(cons(y0, y1), y2))))) -> c5(MARK(s(length(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(tt, y0))))) -> c5(MARK(s(length(and(tt, y0))))) A__LENGTH(cons(z0, s(length(and(s(y0), y1))))) -> c5(MARK(s(length(and(s(y0), y1))))) A__LENGTH(cons(z0, s(length(and(y0, y1))))) -> c5(MARK(s(length(and(y0, y1))))) A__LENGTH(cons(z0, s(length(and(zeros, y0))))) -> c5(MARK(s(length(and(zeros, y0))))) A__LENGTH(cons(z0, s(length(length(zeros))))) -> c5(MARK(s(length(length(zeros))))) A__LENGTH(cons(z0, s(length(length(and(y0, y1)))))) -> c5(MARK(s(length(length(and(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(length(y0)))))) -> c5(MARK(s(length(length(length(y0)))))) A__LENGTH(cons(z0, s(length(length(cons(y0, y1)))))) -> c5(MARK(s(length(length(cons(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(s(y0)))))) -> c5(MARK(s(length(length(s(y0)))))) A__LENGTH(cons(z0, s(length(length(y0))))) -> c5(MARK(s(length(length(y0))))) A__LENGTH(cons(z0, s(length(zeros)))) -> c5(MARK(s(length(zeros)))) A__LENGTH(cons(z0, s(cons(cons(y0, y1), y2)))) -> c5(MARK(s(cons(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(cons(s(y0), y1)))) -> c5(MARK(s(cons(s(y0), y1)))) A__LENGTH(cons(z0, s(cons(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(tt, y0), y1)))) -> c5(MARK(s(cons(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(cons(and(s(y0), y1), y2)))) -> c5(MARK(s(cons(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(length(cons(y0, y1)), y2)))) -> c5(MARK(s(cons(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(s(y0)), y1)))) -> c5(MARK(s(cons(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(cons(and(and(and(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(and(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(length(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(length(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(cons(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(tt, y0), y1), y2)))) -> c5(MARK(s(cons(and(and(tt, y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(and(s(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(s(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(zeros), y0), y1)))) -> c5(MARK(s(cons(and(length(zeros), y0), y1)))) A__LENGTH(cons(z0, s(cons(and(length(and(y0, y1)), y2), y3)))) -> c5(MARK(s(cons(and(length(and(y0, y1)), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(length(y0)), y1), y2)))) -> c5(MARK(s(cons(and(length(length(y0)), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(length(cons(y0, y1)), y2), y3)))) -> c5(MARK(s(cons(and(length(cons(y0, y1)), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(s(y0)), y1), y2)))) -> c5(MARK(s(cons(and(length(s(y0)), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(length(y0), y1), y2)))) -> c5(MARK(s(cons(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(and(zeros, y0), y1), y2)))) -> c5(MARK(s(cons(and(and(zeros, y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(length(and(and(y0, y1), y2)), y3)))) -> c5(MARK(s(cons(length(and(and(y0, y1), y2)), y3)))) A__LENGTH(cons(z0, s(cons(length(and(length(y0), y1)), y2)))) -> c5(MARK(s(cons(length(and(length(y0), y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(cons(y0, y1), y2)), y3)))) -> c5(MARK(s(cons(length(and(cons(y0, y1), y2)), y3)))) A__LENGTH(cons(z0, s(cons(length(and(tt, y0)), y1)))) -> c5(MARK(s(cons(length(and(tt, y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(and(s(y0), y1)), y2)))) -> c5(MARK(s(cons(length(and(s(y0), y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(y0, y1)), y2)))) -> c5(MARK(s(cons(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(zeros, y0)), y1)))) -> c5(MARK(s(cons(length(and(zeros, y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(length(zeros)), y0)))) -> c5(MARK(s(cons(length(length(zeros)), y0)))) A__LENGTH(cons(z0, s(cons(length(length(and(y0, y1))), y2)))) -> c5(MARK(s(cons(length(length(and(y0, y1))), y2)))) A__LENGTH(cons(z0, s(cons(length(length(length(y0))), y1)))) -> c5(MARK(s(cons(length(length(length(y0))), y1)))) A__LENGTH(cons(z0, s(cons(length(length(cons(y0, y1))), y2)))) -> c5(MARK(s(cons(length(length(cons(y0, y1))), y2)))) A__LENGTH(cons(z0, s(cons(length(length(s(y0))), y1)))) -> c5(MARK(s(cons(length(length(s(y0))), y1)))) A__LENGTH(cons(z0, s(cons(length(length(y0)), y1)))) -> c5(MARK(s(cons(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(zeros), y0)))) -> c5(MARK(s(cons(length(zeros), y0)))) MARK(and(cons(cons(y0, y1), z1), z2)) -> c8(MARK(cons(cons(y0, y1), z1))) MARK(and(cons(s(y0), z1), z2)) -> c8(MARK(cons(s(y0), z1))) MARK(and(cons(and(cons(y0, y1), y2), z1), z2)) -> c8(MARK(cons(and(cons(y0, y1), y2), z1))) MARK(and(cons(and(tt, y0), z1), z2)) -> c8(MARK(cons(and(tt, y0), z1))) MARK(and(cons(and(s(y0), y1), z1), z2)) -> c8(MARK(cons(and(s(y0), y1), z1))) MARK(and(cons(length(cons(y0, y1)), z1), z2)) -> c8(MARK(cons(length(cons(y0, y1)), z1))) MARK(and(cons(length(s(y0)), z1), z2)) -> c8(MARK(cons(length(s(y0)), z1))) MARK(and(cons(and(and(and(y0, y1), y2), y3), z1), z2)) -> c8(MARK(cons(and(and(and(y0, y1), y2), y3), z1))) MARK(and(cons(and(and(length(y0), y1), y2), z1), z2)) -> c8(MARK(cons(and(and(length(y0), y1), y2), z1))) MARK(and(cons(and(and(cons(y0, y1), y2), y3), z1), z2)) -> c8(MARK(cons(and(and(cons(y0, y1), y2), y3), z1))) MARK(and(cons(and(and(tt, y0), y1), z1), z2)) -> c8(MARK(cons(and(and(tt, y0), y1), z1))) MARK(and(cons(and(and(s(y0), y1), y2), z1), z2)) -> c8(MARK(cons(and(and(s(y0), y1), y2), z1))) MARK(and(cons(and(and(y0, y1), y2), z1), z2)) -> c8(MARK(cons(and(and(y0, y1), y2), z1))) MARK(and(cons(and(length(zeros), y0), z1), z2)) -> c8(MARK(cons(and(length(zeros), y0), z1))) MARK(and(cons(and(length(and(y0, y1)), y2), z1), z2)) -> c8(MARK(cons(and(length(and(y0, y1)), y2), z1))) MARK(and(cons(and(length(length(y0)), y1), z1), z2)) -> c8(MARK(cons(and(length(length(y0)), y1), z1))) MARK(and(cons(and(length(cons(y0, y1)), y2), z1), z2)) -> c8(MARK(cons(and(length(cons(y0, y1)), y2), z1))) MARK(and(cons(and(length(s(y0)), y1), z1), z2)) -> c8(MARK(cons(and(length(s(y0)), y1), z1))) MARK(and(cons(and(length(y0), y1), z1), z2)) -> c8(MARK(cons(and(length(y0), y1), z1))) MARK(and(cons(and(and(zeros, y0), y1), z1), z2)) -> c8(MARK(cons(and(and(zeros, y0), y1), z1))) MARK(and(cons(length(and(and(y0, y1), y2)), z1), z2)) -> c8(MARK(cons(length(and(and(y0, y1), y2)), z1))) MARK(and(cons(length(and(length(y0), y1)), z1), z2)) -> c8(MARK(cons(length(and(length(y0), y1)), z1))) MARK(and(cons(length(and(cons(y0, y1), y2)), z1), z2)) -> c8(MARK(cons(length(and(cons(y0, y1), y2)), z1))) MARK(and(cons(length(and(tt, y0)), z1), z2)) -> c8(MARK(cons(length(and(tt, y0)), z1))) MARK(and(cons(length(and(s(y0), y1)), z1), z2)) -> c8(MARK(cons(length(and(s(y0), y1)), z1))) MARK(and(cons(length(and(y0, y1)), z1), z2)) -> c8(MARK(cons(length(and(y0, y1)), z1))) MARK(and(cons(length(and(zeros, y0)), z1), z2)) -> c8(MARK(cons(length(and(zeros, y0)), z1))) MARK(and(cons(length(length(zeros)), z1), z2)) -> c8(MARK(cons(length(length(zeros)), z1))) MARK(and(cons(length(length(and(y0, y1))), z1), z2)) -> c8(MARK(cons(length(length(and(y0, y1))), z1))) MARK(and(cons(length(length(length(y0))), z1), z2)) -> c8(MARK(cons(length(length(length(y0))), z1))) MARK(and(cons(length(length(cons(y0, y1))), z1), z2)) -> c8(MARK(cons(length(length(cons(y0, y1))), z1))) MARK(and(cons(length(length(s(y0))), z1), z2)) -> c8(MARK(cons(length(length(s(y0))), z1))) MARK(and(cons(length(length(y0)), z1), z2)) -> c8(MARK(cons(length(length(y0)), z1))) MARK(and(cons(length(zeros), z1), z2)) -> c8(MARK(cons(length(zeros), z1))) MARK(and(tt, cons(y0, y1))) -> c8(A__AND(tt, cons(y0, y1))) MARK(and(tt, s(y0))) -> c8(A__AND(tt, s(y0))) MARK(and(tt, and(cons(y0, y1), y2))) -> c8(A__AND(tt, and(cons(y0, y1), y2))) MARK(and(tt, and(tt, y0))) -> c8(A__AND(tt, and(tt, y0))) MARK(and(tt, and(s(y0), y1))) -> c8(A__AND(tt, and(s(y0), y1))) MARK(and(tt, length(cons(y0, y1)))) -> c8(A__AND(tt, length(cons(y0, y1)))) MARK(and(tt, length(s(y0)))) -> c8(A__AND(tt, length(s(y0)))) MARK(and(tt, and(and(and(y0, y1), y2), y3))) -> c8(A__AND(tt, and(and(and(y0, y1), y2), y3))) MARK(and(tt, and(and(length(y0), y1), y2))) -> c8(A__AND(tt, and(and(length(y0), y1), y2))) MARK(and(tt, and(and(cons(y0, y1), y2), y3))) -> c8(A__AND(tt, and(and(cons(y0, y1), y2), y3))) MARK(and(tt, and(and(tt, y0), y1))) -> c8(A__AND(tt, and(and(tt, y0), y1))) MARK(and(tt, and(and(s(y0), y1), y2))) -> c8(A__AND(tt, and(and(s(y0), y1), y2))) MARK(and(tt, and(and(y0, y1), y2))) -> c8(A__AND(tt, and(and(y0, y1), y2))) MARK(and(tt, and(length(zeros), y0))) -> c8(A__AND(tt, and(length(zeros), y0))) MARK(and(tt, and(length(and(y0, y1)), y2))) -> c8(A__AND(tt, and(length(and(y0, y1)), y2))) MARK(and(tt, and(length(length(y0)), y1))) -> c8(A__AND(tt, and(length(length(y0)), y1))) MARK(and(tt, and(length(cons(y0, y1)), y2))) -> c8(A__AND(tt, and(length(cons(y0, y1)), y2))) MARK(and(tt, and(length(s(y0)), y1))) -> c8(A__AND(tt, and(length(s(y0)), y1))) MARK(and(tt, and(length(y0), y1))) -> c8(A__AND(tt, and(length(y0), y1))) MARK(and(tt, and(and(zeros, y0), y1))) -> c8(A__AND(tt, and(and(zeros, y0), y1))) MARK(and(tt, length(and(and(y0, y1), y2)))) -> c8(A__AND(tt, length(and(and(y0, y1), y2)))) MARK(and(tt, length(and(length(y0), y1)))) -> c8(A__AND(tt, length(and(length(y0), y1)))) MARK(and(tt, length(and(cons(y0, y1), y2)))) -> c8(A__AND(tt, length(and(cons(y0, y1), y2)))) MARK(and(tt, length(and(tt, y0)))) -> c8(A__AND(tt, length(and(tt, y0)))) MARK(and(tt, length(and(s(y0), y1)))) -> c8(A__AND(tt, length(and(s(y0), y1)))) MARK(and(tt, length(and(y0, y1)))) -> c8(A__AND(tt, length(and(y0, y1)))) MARK(and(tt, length(and(zeros, y0)))) -> c8(A__AND(tt, length(and(zeros, y0)))) MARK(and(tt, length(length(zeros)))) -> c8(A__AND(tt, length(length(zeros)))) MARK(and(tt, length(length(and(y0, y1))))) -> c8(A__AND(tt, length(length(and(y0, y1))))) MARK(and(tt, length(length(length(y0))))) -> c8(A__AND(tt, length(length(length(y0))))) MARK(and(tt, length(length(cons(y0, y1))))) -> c8(A__AND(tt, length(length(cons(y0, y1))))) MARK(and(tt, length(length(s(y0))))) -> c8(A__AND(tt, length(length(s(y0))))) MARK(and(tt, length(length(y0)))) -> c8(A__AND(tt, length(length(y0)))) MARK(and(tt, length(zeros))) -> c8(A__AND(tt, length(zeros))) MARK(and(s(s(y0)), z1)) -> c8(MARK(s(s(y0)))) MARK(and(s(and(cons(y0, y1), y2)), z1)) -> c8(MARK(s(and(cons(y0, y1), y2)))) MARK(and(s(and(tt, y0)), z1)) -> c8(MARK(s(and(tt, y0)))) MARK(and(s(and(s(y0), y1)), z1)) -> c8(MARK(s(and(s(y0), y1)))) MARK(and(s(length(cons(y0, y1))), z1)) -> c8(MARK(s(length(cons(y0, y1))))) MARK(and(s(length(s(y0))), z1)) -> c8(MARK(s(length(s(y0))))) MARK(and(s(and(and(and(y0, y1), y2), y3)), z1)) -> c8(MARK(s(and(and(and(y0, y1), y2), y3)))) MARK(and(s(and(and(length(y0), y1), y2)), z1)) -> c8(MARK(s(and(and(length(y0), y1), y2)))) MARK(and(s(and(and(cons(y0, y1), y2), y3)), z1)) -> c8(MARK(s(and(and(cons(y0, y1), y2), y3)))) MARK(and(s(and(and(tt, y0), y1)), z1)) -> c8(MARK(s(and(and(tt, y0), y1)))) MARK(and(s(and(and(s(y0), y1), y2)), z1)) -> c8(MARK(s(and(and(s(y0), y1), y2)))) MARK(and(s(and(and(y0, y1), y2)), z1)) -> c8(MARK(s(and(and(y0, y1), y2)))) MARK(and(s(and(length(zeros), y0)), z1)) -> c8(MARK(s(and(length(zeros), y0)))) MARK(and(s(and(length(and(y0, y1)), y2)), z1)) -> c8(MARK(s(and(length(and(y0, y1)), y2)))) MARK(and(s(and(length(length(y0)), y1)), z1)) -> c8(MARK(s(and(length(length(y0)), y1)))) MARK(and(s(and(length(cons(y0, y1)), y2)), z1)) -> c8(MARK(s(and(length(cons(y0, y1)), y2)))) MARK(and(s(and(length(s(y0)), y1)), z1)) -> c8(MARK(s(and(length(s(y0)), y1)))) MARK(and(s(and(length(y0), y1)), z1)) -> c8(MARK(s(and(length(y0), y1)))) MARK(and(s(and(and(zeros, y0), y1)), z1)) -> c8(MARK(s(and(and(zeros, y0), y1)))) MARK(and(s(length(and(and(y0, y1), y2))), z1)) -> c8(MARK(s(length(and(and(y0, y1), y2))))) MARK(and(s(length(and(length(y0), y1))), z1)) -> c8(MARK(s(length(and(length(y0), y1))))) MARK(and(s(length(and(cons(y0, y1), y2))), z1)) -> c8(MARK(s(length(and(cons(y0, y1), y2))))) MARK(and(s(length(and(tt, y0))), z1)) -> c8(MARK(s(length(and(tt, y0))))) MARK(and(s(length(and(s(y0), y1))), z1)) -> c8(MARK(s(length(and(s(y0), y1))))) MARK(and(s(length(and(y0, y1))), z1)) -> c8(MARK(s(length(and(y0, y1))))) MARK(and(s(length(and(zeros, y0))), z1)) -> c8(MARK(s(length(and(zeros, y0))))) MARK(and(s(length(length(zeros))), z1)) -> c8(MARK(s(length(length(zeros))))) MARK(and(s(length(length(and(y0, y1)))), z1)) -> c8(MARK(s(length(length(and(y0, y1)))))) MARK(and(s(length(length(length(y0)))), z1)) -> c8(MARK(s(length(length(length(y0)))))) MARK(and(s(length(length(cons(y0, y1)))), z1)) -> c8(MARK(s(length(length(cons(y0, y1)))))) MARK(and(s(length(length(s(y0)))), z1)) -> c8(MARK(s(length(length(s(y0)))))) MARK(and(s(length(length(y0))), z1)) -> c8(MARK(s(length(length(y0))))) MARK(and(s(length(zeros)), z1)) -> c8(MARK(s(length(zeros)))) MARK(and(s(cons(cons(y0, y1), y2)), z1)) -> c8(MARK(s(cons(cons(y0, y1), y2)))) MARK(and(s(cons(s(y0), y1)), z1)) -> c8(MARK(s(cons(s(y0), y1)))) MARK(and(s(cons(and(cons(y0, y1), y2), y3)), z1)) -> c8(MARK(s(cons(and(cons(y0, y1), y2), y3)))) MARK(and(s(cons(and(tt, y0), y1)), z1)) -> c8(MARK(s(cons(and(tt, y0), y1)))) MARK(and(s(cons(and(s(y0), y1), y2)), z1)) -> c8(MARK(s(cons(and(s(y0), y1), y2)))) MARK(and(s(cons(length(cons(y0, y1)), y2)), z1)) -> c8(MARK(s(cons(length(cons(y0, y1)), y2)))) MARK(and(s(cons(length(s(y0)), y1)), z1)) -> c8(MARK(s(cons(length(s(y0)), y1)))) MARK(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), z1)) -> c8(MARK(s(cons(and(and(and(y0, y1), y2), y3), y4)))) MARK(and(s(cons(and(and(length(y0), y1), y2), y3)), z1)) -> c8(MARK(s(cons(and(and(length(y0), y1), y2), y3)))) MARK(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), z1)) -> c8(MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) MARK(and(s(cons(and(and(tt, y0), y1), y2)), z1)) -> c8(MARK(s(cons(and(and(tt, y0), y1), y2)))) MARK(and(s(cons(and(and(s(y0), y1), y2), y3)), z1)) -> c8(MARK(s(cons(and(and(s(y0), y1), y2), y3)))) MARK(and(s(cons(and(and(y0, y1), y2), y3)), z1)) -> c8(MARK(s(cons(and(and(y0, y1), y2), y3)))) MARK(and(s(cons(and(length(zeros), y0), y1)), z1)) -> c8(MARK(s(cons(and(length(zeros), y0), y1)))) MARK(and(s(cons(and(length(and(y0, y1)), y2), y3)), z1)) -> c8(MARK(s(cons(and(length(and(y0, y1)), y2), y3)))) MARK(and(s(cons(and(length(length(y0)), y1), y2)), z1)) -> c8(MARK(s(cons(and(length(length(y0)), y1), y2)))) MARK(and(s(cons(and(length(cons(y0, y1)), y2), y3)), z1)) -> c8(MARK(s(cons(and(length(cons(y0, y1)), y2), y3)))) MARK(and(s(cons(and(length(s(y0)), y1), y2)), z1)) -> c8(MARK(s(cons(and(length(s(y0)), y1), y2)))) MARK(and(s(cons(and(length(y0), y1), y2)), z1)) -> c8(MARK(s(cons(and(length(y0), y1), y2)))) MARK(and(s(cons(and(and(zeros, y0), y1), y2)), z1)) -> c8(MARK(s(cons(and(and(zeros, y0), y1), y2)))) MARK(and(s(cons(length(and(and(y0, y1), y2)), y3)), z1)) -> c8(MARK(s(cons(length(and(and(y0, y1), y2)), y3)))) MARK(and(s(cons(length(and(length(y0), y1)), y2)), z1)) -> c8(MARK(s(cons(length(and(length(y0), y1)), y2)))) MARK(and(s(cons(length(and(cons(y0, y1), y2)), y3)), z1)) -> c8(MARK(s(cons(length(and(cons(y0, y1), y2)), y3)))) MARK(and(s(cons(length(and(tt, y0)), y1)), z1)) -> c8(MARK(s(cons(length(and(tt, y0)), y1)))) MARK(and(s(cons(length(and(s(y0), y1)), y2)), z1)) -> c8(MARK(s(cons(length(and(s(y0), y1)), y2)))) MARK(and(s(cons(length(and(y0, y1)), y2)), z1)) -> c8(MARK(s(cons(length(and(y0, y1)), y2)))) MARK(and(s(cons(length(and(zeros, y0)), y1)), z1)) -> c8(MARK(s(cons(length(and(zeros, y0)), y1)))) MARK(and(s(cons(length(length(zeros)), y0)), z1)) -> c8(MARK(s(cons(length(length(zeros)), y0)))) MARK(and(s(cons(length(length(and(y0, y1))), y2)), z1)) -> c8(MARK(s(cons(length(length(and(y0, y1))), y2)))) MARK(and(s(cons(length(length(length(y0))), y1)), z1)) -> c8(MARK(s(cons(length(length(length(y0))), y1)))) MARK(and(s(cons(length(length(cons(y0, y1))), y2)), z1)) -> c8(MARK(s(cons(length(length(cons(y0, y1))), y2)))) MARK(and(s(cons(length(length(s(y0))), y1)), z1)) -> c8(MARK(s(cons(length(length(s(y0))), y1)))) MARK(and(s(cons(length(length(y0)), y1)), z1)) -> c8(MARK(s(cons(length(length(y0)), y1)))) MARK(and(s(cons(length(zeros), y0)), z1)) -> c8(MARK(s(cons(length(zeros), y0)))) S tuples: A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c9(MARK(s(z0))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) MARK(cons(and(and(cons(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(cons(y0, y1), y2), y3))) MARK(cons(and(and(tt, y0), y1), z1)) -> c10(MARK(and(and(tt, y0), y1))) MARK(cons(and(and(s(y0), y1), y2), z1)) -> c10(MARK(and(and(s(y0), y1), y2))) MARK(cons(and(and(y0, y1), y2), z1)) -> c10(MARK(and(and(y0, y1), y2))) MARK(cons(and(length(zeros), y0), z1)) -> c10(MARK(and(length(zeros), y0))) MARK(cons(and(length(and(y0, y1)), y2), z1)) -> c10(MARK(and(length(and(y0, y1)), y2))) MARK(cons(and(length(length(y0)), y1), z1)) -> c10(MARK(and(length(length(y0)), y1))) MARK(cons(and(length(cons(y0, y1)), y2), z1)) -> c10(MARK(and(length(cons(y0, y1)), y2))) MARK(cons(and(length(s(y0)), y1), z1)) -> c10(MARK(and(length(s(y0)), y1))) MARK(cons(and(length(y0), y1), z1)) -> c10(MARK(and(length(y0), y1))) MARK(cons(and(and(zeros, y0), y1), z1)) -> c10(MARK(and(and(zeros, y0), y1))) MARK(cons(length(and(and(y0, y1), y2)), z1)) -> c10(MARK(length(and(and(y0, y1), y2)))) MARK(cons(length(and(length(y0), y1)), z1)) -> c10(MARK(length(and(length(y0), y1)))) MARK(cons(length(and(cons(y0, y1), y2)), z1)) -> c10(MARK(length(and(cons(y0, y1), y2)))) MARK(cons(length(and(tt, y0)), z1)) -> c10(MARK(length(and(tt, y0)))) MARK(cons(length(and(s(y0), 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MARK(s(length(s(y0)))) -> c14(MARK(length(s(y0)))) MARK(s(and(and(and(y0, y1), y2), y3))) -> c14(MARK(and(and(and(y0, y1), y2), y3))) MARK(s(and(and(length(y0), y1), y2))) -> c14(MARK(and(and(length(y0), y1), y2))) MARK(s(and(and(cons(y0, y1), y2), y3))) -> c14(MARK(and(and(cons(y0, y1), y2), y3))) MARK(s(and(and(tt, y0), y1))) -> c14(MARK(and(and(tt, y0), y1))) MARK(s(and(and(s(y0), y1), y2))) -> c14(MARK(and(and(s(y0), y1), y2))) MARK(s(and(and(y0, y1), y2))) -> c14(MARK(and(and(y0, y1), y2))) MARK(s(and(length(zeros), y0))) -> c14(MARK(and(length(zeros), y0))) MARK(s(and(length(and(y0, y1)), y2))) -> c14(MARK(and(length(and(y0, y1)), y2))) MARK(s(and(length(length(y0)), y1))) -> c14(MARK(and(length(length(y0)), y1))) MARK(s(and(length(cons(y0, y1)), y2))) -> c14(MARK(and(length(cons(y0, y1)), y2))) MARK(s(and(length(s(y0)), y1))) -> c14(MARK(and(length(s(y0)), y1))) MARK(s(and(length(y0), y1))) -> c14(MARK(and(length(y0), y1))) MARK(s(and(and(zeros, y0), y1))) -> c14(MARK(and(and(zeros, y0), y1))) MARK(s(length(and(and(y0, y1), y2)))) -> c14(MARK(length(and(and(y0, y1), y2)))) MARK(s(length(and(length(y0), y1)))) -> c14(MARK(length(and(length(y0), y1)))) MARK(s(length(and(cons(y0, y1), y2)))) -> c14(MARK(length(and(cons(y0, y1), y2)))) MARK(s(length(and(tt, y0)))) -> c14(MARK(length(and(tt, y0)))) MARK(s(length(and(s(y0), y1)))) -> c14(MARK(length(and(s(y0), y1)))) MARK(s(length(and(y0, y1)))) -> c14(MARK(length(and(y0, y1)))) MARK(s(length(and(zeros, y0)))) -> c14(MARK(length(and(zeros, y0)))) MARK(s(length(length(zeros)))) -> c14(MARK(length(length(zeros)))) MARK(s(length(length(and(y0, y1))))) -> c14(MARK(length(length(and(y0, y1))))) MARK(s(length(length(length(y0))))) -> c14(MARK(length(length(length(y0))))) MARK(s(length(length(cons(y0, y1))))) -> c14(MARK(length(length(cons(y0, y1))))) MARK(s(length(length(s(y0))))) -> c14(MARK(length(length(s(y0))))) MARK(s(length(length(y0)))) -> c14(MARK(length(length(y0)))) MARK(s(length(zeros))) -> c14(MARK(length(zeros))) MARK(s(cons(cons(y0, y1), y2))) -> c14(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c14(MARK(cons(s(y0), y1))) MARK(s(cons(and(cons(y0, y1), y2), y3))) -> c14(MARK(cons(and(cons(y0, y1), y2), y3))) MARK(s(cons(and(tt, y0), y1))) -> c14(MARK(cons(and(tt, y0), y1))) MARK(s(cons(and(s(y0), y1), y2))) -> c14(MARK(cons(and(s(y0), y1), y2))) MARK(s(cons(length(cons(y0, y1)), y2))) -> c14(MARK(cons(length(cons(y0, y1)), y2))) MARK(s(cons(length(s(y0)), y1))) -> c14(MARK(cons(length(s(y0)), y1))) MARK(s(cons(and(and(and(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(and(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(length(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(length(y0), y1), y2), y3))) MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(cons(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(tt, y0), y1), y2))) -> c14(MARK(cons(and(and(tt, y0), y1), y2))) MARK(s(cons(and(and(s(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(s(y0), y1), y2), y3))) MARK(s(cons(and(and(y0, y1), y2), y3))) -> c14(MARK(cons(and(and(y0, y1), y2), y3))) MARK(s(cons(and(length(zeros), y0), y1))) -> c14(MARK(cons(and(length(zeros), y0), y1))) MARK(s(cons(and(length(and(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(and(y0, y1)), y2), y3))) MARK(s(cons(and(length(length(y0)), y1), y2))) -> c14(MARK(cons(and(length(length(y0)), y1), y2))) MARK(s(cons(and(length(cons(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(cons(y0, y1)), y2), y3))) MARK(s(cons(and(length(s(y0)), y1), y2))) -> c14(MARK(cons(and(length(s(y0)), y1), y2))) MARK(s(cons(and(length(y0), y1), y2))) -> c14(MARK(cons(and(length(y0), y1), y2))) MARK(s(cons(and(and(zeros, y0), y1), y2))) -> c14(MARK(cons(and(and(zeros, y0), y1), y2))) MARK(s(cons(length(and(and(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(and(y0, y1), y2)), y3))) MARK(s(cons(length(and(length(y0), y1)), y2))) -> c14(MARK(cons(length(and(length(y0), y1)), y2))) MARK(s(cons(length(and(cons(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(cons(y0, y1), y2)), y3))) MARK(s(cons(length(and(tt, y0)), y1))) -> c14(MARK(cons(length(and(tt, y0)), y1))) MARK(s(cons(length(and(s(y0), y1)), y2))) -> c14(MARK(cons(length(and(s(y0), y1)), y2))) MARK(s(cons(length(and(y0, y1)), y2))) -> c14(MARK(cons(length(and(y0, y1)), y2))) MARK(s(cons(length(and(zeros, y0)), y1))) -> c14(MARK(cons(length(and(zeros, y0)), y1))) MARK(s(cons(length(length(zeros)), y0))) -> c14(MARK(cons(length(length(zeros)), y0))) MARK(s(cons(length(length(and(y0, y1))), y2))) -> c14(MARK(cons(length(length(and(y0, y1))), y2))) MARK(s(cons(length(length(length(y0))), y1))) -> c14(MARK(cons(length(length(length(y0))), y1))) MARK(s(cons(length(length(cons(y0, y1))), y2))) -> c14(MARK(cons(length(length(cons(y0, y1))), y2))) MARK(s(cons(length(length(s(y0))), y1))) -> c14(MARK(cons(length(length(s(y0))), y1))) MARK(s(cons(length(length(y0)), y1))) -> c14(MARK(cons(length(length(y0)), y1))) MARK(s(cons(length(zeros), y0))) -> c14(MARK(cons(length(zeros), y0))) A__LENGTH(cons(z0, s(s(y0)))) -> c5(MARK(s(s(y0)))) A__LENGTH(cons(z0, s(and(cons(y0, y1), y2)))) -> c5(MARK(s(and(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(tt, y0)))) -> c5(MARK(s(and(tt, y0)))) A__LENGTH(cons(z0, s(and(s(y0), y1)))) -> c5(MARK(s(and(s(y0), y1)))) A__LENGTH(cons(z0, s(length(cons(y0, y1))))) -> c5(MARK(s(length(cons(y0, y1))))) A__LENGTH(cons(z0, s(length(s(y0))))) -> c5(MARK(s(length(s(y0))))) A__LENGTH(cons(z0, s(and(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(length(y0), y1), y2)))) -> c5(MARK(s(and(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(tt, y0), y1)))) -> c5(MARK(s(and(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(and(and(s(y0), y1), y2)))) -> c5(MARK(s(and(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(y0, y1), y2)))) -> c5(MARK(s(and(and(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(length(zeros), y0)))) -> c5(MARK(s(and(length(zeros), y0)))) A__LENGTH(cons(z0, s(and(length(and(y0, y1)), y2)))) -> c5(MARK(s(and(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(length(y0)), y1)))) -> c5(MARK(s(and(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(cons(y0, y1)), y2)))) -> c5(MARK(s(and(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(s(y0)), y1)))) -> c5(MARK(s(and(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(y0), y1)))) -> c5(MARK(s(and(length(y0), y1)))) A__LENGTH(cons(z0, s(and(and(zeros, y0), y1)))) -> c5(MARK(s(and(and(zeros, y0), y1)))) A__LENGTH(cons(z0, s(length(and(and(y0, y1), y2))))) -> c5(MARK(s(length(and(and(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(length(y0), y1))))) -> c5(MARK(s(length(and(length(y0), y1))))) A__LENGTH(cons(z0, s(length(and(cons(y0, y1), y2))))) -> c5(MARK(s(length(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(tt, y0))))) -> 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z1)) -> c8(MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) MARK(and(s(cons(and(and(tt, y0), y1), y2)), z1)) -> c8(MARK(s(cons(and(and(tt, y0), y1), y2)))) MARK(and(s(cons(and(and(s(y0), y1), y2), y3)), z1)) -> c8(MARK(s(cons(and(and(s(y0), y1), y2), y3)))) MARK(and(s(cons(and(and(y0, y1), y2), y3)), z1)) -> c8(MARK(s(cons(and(and(y0, y1), y2), y3)))) MARK(and(s(cons(and(length(zeros), y0), y1)), z1)) -> c8(MARK(s(cons(and(length(zeros), y0), y1)))) MARK(and(s(cons(and(length(and(y0, y1)), y2), y3)), z1)) -> c8(MARK(s(cons(and(length(and(y0, y1)), y2), y3)))) MARK(and(s(cons(and(length(length(y0)), y1), y2)), z1)) -> c8(MARK(s(cons(and(length(length(y0)), y1), y2)))) MARK(and(s(cons(and(length(cons(y0, y1)), y2), y3)), z1)) -> c8(MARK(s(cons(and(length(cons(y0, y1)), y2), y3)))) MARK(and(s(cons(and(length(s(y0)), y1), y2)), z1)) -> c8(MARK(s(cons(and(length(s(y0)), y1), y2)))) MARK(and(s(cons(and(length(y0), y1), y2)), z1)) -> c8(MARK(s(cons(and(length(y0), y1), y2)))) MARK(and(s(cons(and(and(zeros, y0), y1), y2)), z1)) -> c8(MARK(s(cons(and(and(zeros, y0), y1), y2)))) MARK(and(s(cons(length(and(and(y0, y1), y2)), y3)), z1)) -> c8(MARK(s(cons(length(and(and(y0, y1), y2)), y3)))) MARK(and(s(cons(length(and(length(y0), y1)), y2)), z1)) -> c8(MARK(s(cons(length(and(length(y0), y1)), y2)))) MARK(and(s(cons(length(and(cons(y0, y1), y2)), y3)), z1)) -> c8(MARK(s(cons(length(and(cons(y0, y1), y2)), y3)))) MARK(and(s(cons(length(and(tt, y0)), y1)), z1)) -> c8(MARK(s(cons(length(and(tt, y0)), y1)))) MARK(and(s(cons(length(and(s(y0), y1)), y2)), z1)) -> c8(MARK(s(cons(length(and(s(y0), y1)), y2)))) MARK(and(s(cons(length(and(y0, y1)), y2)), z1)) -> c8(MARK(s(cons(length(and(y0, y1)), y2)))) MARK(and(s(cons(length(and(zeros, y0)), y1)), z1)) -> c8(MARK(s(cons(length(and(zeros, y0)), y1)))) MARK(and(s(cons(length(length(zeros)), y0)), z1)) -> c8(MARK(s(cons(length(length(zeros)), y0)))) MARK(and(s(cons(length(length(and(y0, y1))), y2)), z1)) -> c8(MARK(s(cons(length(length(and(y0, y1))), y2)))) MARK(and(s(cons(length(length(length(y0))), y1)), z1)) -> c8(MARK(s(cons(length(length(length(y0))), y1)))) MARK(and(s(cons(length(length(cons(y0, y1))), y2)), z1)) -> c8(MARK(s(cons(length(length(cons(y0, y1))), y2)))) MARK(and(s(cons(length(length(s(y0))), y1)), z1)) -> c8(MARK(s(cons(length(length(s(y0))), y1)))) MARK(and(s(cons(length(length(y0)), y1)), z1)) -> c8(MARK(s(cons(length(length(y0)), y1)))) MARK(and(s(cons(length(zeros), y0)), z1)) -> c8(MARK(s(cons(length(zeros), y0)))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__LENGTH_1, MARK_1, A__AND_2 Compound Symbols: c5_2, c9_2, c9_1, c5_1, c8_2, c8_1, c2_1, c10_1, c14_1 ---------------------------------------- (179) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(length(s(z0))) -> c9(MARK(s(z0))) by MARK(length(s(s(y0)))) -> c9(MARK(s(s(y0)))) MARK(length(s(and(cons(y0, y1), y2)))) -> c9(MARK(s(and(cons(y0, y1), y2)))) MARK(length(s(and(tt, y0)))) -> c9(MARK(s(and(tt, y0)))) MARK(length(s(and(s(y0), y1)))) -> c9(MARK(s(and(s(y0), y1)))) MARK(length(s(length(cons(y0, y1))))) -> c9(MARK(s(length(cons(y0, y1))))) MARK(length(s(length(s(y0))))) -> c9(MARK(s(length(s(y0))))) MARK(length(s(and(and(and(y0, y1), y2), y3)))) -> c9(MARK(s(and(and(and(y0, y1), y2), y3)))) MARK(length(s(and(and(length(y0), y1), y2)))) -> c9(MARK(s(and(and(length(y0), y1), y2)))) MARK(length(s(and(and(cons(y0, y1), y2), y3)))) -> c9(MARK(s(and(and(cons(y0, y1), y2), y3)))) MARK(length(s(and(and(tt, y0), y1)))) -> c9(MARK(s(and(and(tt, y0), y1)))) MARK(length(s(and(and(s(y0), y1), y2)))) -> c9(MARK(s(and(and(s(y0), y1), y2)))) MARK(length(s(and(and(y0, y1), y2)))) -> c9(MARK(s(and(and(y0, y1), y2)))) MARK(length(s(and(length(zeros), y0)))) -> c9(MARK(s(and(length(zeros), y0)))) MARK(length(s(and(length(and(y0, y1)), y2)))) -> c9(MARK(s(and(length(and(y0, y1)), y2)))) MARK(length(s(and(length(length(y0)), y1)))) -> c9(MARK(s(and(length(length(y0)), y1)))) MARK(length(s(and(length(cons(y0, y1)), y2)))) -> c9(MARK(s(and(length(cons(y0, y1)), y2)))) MARK(length(s(and(length(s(y0)), y1)))) -> c9(MARK(s(and(length(s(y0)), y1)))) MARK(length(s(and(length(y0), y1)))) -> c9(MARK(s(and(length(y0), y1)))) MARK(length(s(and(and(zeros, y0), y1)))) -> c9(MARK(s(and(and(zeros, y0), y1)))) MARK(length(s(length(and(and(y0, y1), y2))))) -> c9(MARK(s(length(and(and(y0, y1), y2))))) MARK(length(s(length(and(length(y0), y1))))) -> c9(MARK(s(length(and(length(y0), y1))))) MARK(length(s(length(and(cons(y0, y1), y2))))) -> c9(MARK(s(length(and(cons(y0, y1), y2))))) MARK(length(s(length(and(tt, y0))))) -> c9(MARK(s(length(and(tt, y0))))) MARK(length(s(length(and(s(y0), y1))))) -> c9(MARK(s(length(and(s(y0), y1))))) MARK(length(s(length(and(y0, y1))))) -> c9(MARK(s(length(and(y0, y1))))) MARK(length(s(length(and(zeros, y0))))) -> c9(MARK(s(length(and(zeros, y0))))) MARK(length(s(length(length(zeros))))) -> c9(MARK(s(length(length(zeros))))) MARK(length(s(length(length(and(y0, y1)))))) -> c9(MARK(s(length(length(and(y0, y1)))))) MARK(length(s(length(length(length(y0)))))) -> c9(MARK(s(length(length(length(y0)))))) MARK(length(s(length(length(cons(y0, y1)))))) -> c9(MARK(s(length(length(cons(y0, y1)))))) MARK(length(s(length(length(s(y0)))))) -> c9(MARK(s(length(length(s(y0)))))) MARK(length(s(length(length(y0))))) -> c9(MARK(s(length(length(y0))))) MARK(length(s(length(zeros)))) -> c9(MARK(s(length(zeros)))) MARK(length(s(cons(cons(y0, y1), y2)))) -> c9(MARK(s(cons(cons(y0, y1), y2)))) MARK(length(s(cons(s(y0), y1)))) -> c9(MARK(s(cons(s(y0), y1)))) MARK(length(s(cons(and(cons(y0, y1), y2), y3)))) -> c9(MARK(s(cons(and(cons(y0, y1), y2), y3)))) MARK(length(s(cons(and(tt, y0), y1)))) -> c9(MARK(s(cons(and(tt, y0), y1)))) MARK(length(s(cons(and(s(y0), y1), y2)))) -> c9(MARK(s(cons(and(s(y0), y1), y2)))) MARK(length(s(cons(length(cons(y0, y1)), y2)))) -> c9(MARK(s(cons(length(cons(y0, y1)), y2)))) MARK(length(s(cons(length(s(y0)), y1)))) -> c9(MARK(s(cons(length(s(y0)), y1)))) MARK(length(s(cons(and(and(and(y0, y1), y2), y3), y4)))) -> c9(MARK(s(cons(and(and(and(y0, y1), y2), y3), y4)))) MARK(length(s(cons(and(and(length(y0), y1), y2), y3)))) -> c9(MARK(s(cons(and(and(length(y0), y1), y2), y3)))) MARK(length(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) -> c9(MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) MARK(length(s(cons(and(and(tt, y0), y1), y2)))) -> c9(MARK(s(cons(and(and(tt, y0), y1), y2)))) MARK(length(s(cons(and(and(s(y0), y1), y2), y3)))) -> c9(MARK(s(cons(and(and(s(y0), y1), y2), y3)))) MARK(length(s(cons(and(and(y0, y1), y2), y3)))) -> c9(MARK(s(cons(and(and(y0, y1), y2), y3)))) MARK(length(s(cons(and(length(zeros), y0), y1)))) -> c9(MARK(s(cons(and(length(zeros), y0), y1)))) MARK(length(s(cons(and(length(and(y0, y1)), y2), y3)))) -> c9(MARK(s(cons(and(length(and(y0, y1)), y2), y3)))) MARK(length(s(cons(and(length(length(y0)), y1), y2)))) -> c9(MARK(s(cons(and(length(length(y0)), y1), y2)))) MARK(length(s(cons(and(length(cons(y0, y1)), y2), y3)))) -> c9(MARK(s(cons(and(length(cons(y0, y1)), y2), y3)))) MARK(length(s(cons(and(length(s(y0)), y1), y2)))) -> c9(MARK(s(cons(and(length(s(y0)), y1), y2)))) MARK(length(s(cons(and(length(y0), y1), y2)))) -> c9(MARK(s(cons(and(length(y0), y1), y2)))) MARK(length(s(cons(and(and(zeros, y0), y1), y2)))) -> c9(MARK(s(cons(and(and(zeros, y0), y1), y2)))) MARK(length(s(cons(length(and(and(y0, y1), y2)), y3)))) -> c9(MARK(s(cons(length(and(and(y0, y1), y2)), y3)))) MARK(length(s(cons(length(and(length(y0), y1)), y2)))) -> c9(MARK(s(cons(length(and(length(y0), y1)), y2)))) MARK(length(s(cons(length(and(cons(y0, y1), y2)), y3)))) -> c9(MARK(s(cons(length(and(cons(y0, y1), y2)), y3)))) MARK(length(s(cons(length(and(tt, y0)), y1)))) -> c9(MARK(s(cons(length(and(tt, y0)), y1)))) MARK(length(s(cons(length(and(s(y0), y1)), y2)))) -> c9(MARK(s(cons(length(and(s(y0), y1)), y2)))) MARK(length(s(cons(length(and(y0, y1)), y2)))) -> c9(MARK(s(cons(length(and(y0, y1)), y2)))) MARK(length(s(cons(length(and(zeros, y0)), y1)))) -> c9(MARK(s(cons(length(and(zeros, y0)), y1)))) MARK(length(s(cons(length(length(zeros)), y0)))) -> c9(MARK(s(cons(length(length(zeros)), y0)))) MARK(length(s(cons(length(length(and(y0, y1))), y2)))) -> c9(MARK(s(cons(length(length(and(y0, y1))), y2)))) MARK(length(s(cons(length(length(length(y0))), y1)))) -> c9(MARK(s(cons(length(length(length(y0))), y1)))) MARK(length(s(cons(length(length(cons(y0, y1))), y2)))) -> c9(MARK(s(cons(length(length(cons(y0, y1))), y2)))) MARK(length(s(cons(length(length(s(y0))), y1)))) -> c9(MARK(s(cons(length(length(s(y0))), y1)))) MARK(length(s(cons(length(length(y0)), y1)))) -> c9(MARK(s(cons(length(length(y0)), y1)))) MARK(length(s(cons(length(zeros), y0)))) -> c9(MARK(s(cons(length(zeros), y0)))) ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) MARK(cons(and(and(cons(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(cons(y0, y1), y2), y3))) MARK(cons(and(and(tt, y0), y1), z1)) -> c10(MARK(and(and(tt, y0), y1))) MARK(cons(and(and(s(y0), y1), y2), z1)) -> c10(MARK(and(and(s(y0), y1), y2))) MARK(cons(and(and(y0, y1), y2), z1)) -> c10(MARK(and(and(y0, y1), y2))) MARK(cons(and(length(zeros), y0), z1)) -> c10(MARK(and(length(zeros), y0))) MARK(cons(and(length(and(y0, y1)), y2), z1)) -> c10(MARK(and(length(and(y0, y1)), y2))) MARK(cons(and(length(length(y0)), y1), z1)) -> 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c9(MARK(s(cons(and(and(s(y0), y1), y2), y3)))) MARK(length(s(cons(and(and(y0, y1), y2), y3)))) -> c9(MARK(s(cons(and(and(y0, y1), y2), y3)))) MARK(length(s(cons(and(length(zeros), y0), y1)))) -> c9(MARK(s(cons(and(length(zeros), y0), y1)))) MARK(length(s(cons(and(length(and(y0, y1)), y2), y3)))) -> c9(MARK(s(cons(and(length(and(y0, y1)), y2), y3)))) MARK(length(s(cons(and(length(length(y0)), y1), y2)))) -> c9(MARK(s(cons(and(length(length(y0)), y1), y2)))) MARK(length(s(cons(and(length(cons(y0, y1)), y2), y3)))) -> c9(MARK(s(cons(and(length(cons(y0, y1)), y2), y3)))) MARK(length(s(cons(and(length(s(y0)), y1), y2)))) -> c9(MARK(s(cons(and(length(s(y0)), y1), y2)))) MARK(length(s(cons(and(length(y0), y1), y2)))) -> c9(MARK(s(cons(and(length(y0), y1), y2)))) MARK(length(s(cons(and(and(zeros, y0), y1), y2)))) -> c9(MARK(s(cons(and(and(zeros, y0), y1), y2)))) MARK(length(s(cons(length(and(and(y0, y1), y2)), y3)))) -> c9(MARK(s(cons(length(and(and(y0, y1), y2)), y3)))) MARK(length(s(cons(length(and(length(y0), y1)), y2)))) -> c9(MARK(s(cons(length(and(length(y0), y1)), y2)))) MARK(length(s(cons(length(and(cons(y0, y1), y2)), y3)))) -> c9(MARK(s(cons(length(and(cons(y0, y1), y2)), y3)))) MARK(length(s(cons(length(and(tt, y0)), y1)))) -> c9(MARK(s(cons(length(and(tt, y0)), y1)))) MARK(length(s(cons(length(and(s(y0), y1)), y2)))) -> c9(MARK(s(cons(length(and(s(y0), y1)), y2)))) MARK(length(s(cons(length(and(y0, y1)), y2)))) -> c9(MARK(s(cons(length(and(y0, y1)), y2)))) MARK(length(s(cons(length(and(zeros, y0)), y1)))) -> c9(MARK(s(cons(length(and(zeros, y0)), y1)))) MARK(length(s(cons(length(length(zeros)), y0)))) -> c9(MARK(s(cons(length(length(zeros)), y0)))) MARK(length(s(cons(length(length(and(y0, y1))), y2)))) -> c9(MARK(s(cons(length(length(and(y0, y1))), y2)))) MARK(length(s(cons(length(length(length(y0))), y1)))) -> c9(MARK(s(cons(length(length(length(y0))), y1)))) MARK(length(s(cons(length(length(cons(y0, y1))), y2)))) -> c9(MARK(s(cons(length(length(cons(y0, y1))), y2)))) MARK(length(s(cons(length(length(s(y0))), y1)))) -> c9(MARK(s(cons(length(length(s(y0))), y1)))) MARK(length(s(cons(length(length(y0)), y1)))) -> c9(MARK(s(cons(length(length(y0)), y1)))) MARK(length(s(cons(length(zeros), y0)))) -> c9(MARK(s(cons(length(zeros), y0)))) S tuples: A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), 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MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) MARK(cons(and(and(cons(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(cons(y0, y1), y2), y3))) MARK(cons(and(and(tt, y0), y1), z1)) -> c10(MARK(and(and(tt, y0), y1))) MARK(cons(and(and(s(y0), y1), y2), z1)) -> c10(MARK(and(and(s(y0), y1), y2))) MARK(cons(and(and(y0, y1), y2), z1)) -> c10(MARK(and(and(y0, y1), y2))) MARK(cons(and(length(zeros), y0), z1)) -> c10(MARK(and(length(zeros), y0))) MARK(cons(and(length(and(y0, y1)), y2), z1)) -> c10(MARK(and(length(and(y0, y1)), y2))) MARK(cons(and(length(length(y0)), y1), z1)) -> c10(MARK(and(length(length(y0)), y1))) MARK(cons(and(length(cons(y0, y1)), y2), z1)) -> c10(MARK(and(length(cons(y0, y1)), y2))) MARK(cons(and(length(s(y0)), y1), z1)) -> c10(MARK(and(length(s(y0)), y1))) MARK(cons(and(length(y0), y1), z1)) -> c10(MARK(and(length(y0), y1))) MARK(cons(and(and(zeros, y0), y1), z1)) -> c10(MARK(and(and(zeros, y0), y1))) MARK(cons(length(and(and(y0, y1), y2)), z1)) -> c10(MARK(length(and(and(y0, y1), y2)))) MARK(cons(length(and(length(y0), y1)), z1)) -> c10(MARK(length(and(length(y0), y1)))) MARK(cons(length(and(cons(y0, y1), y2)), z1)) -> c10(MARK(length(and(cons(y0, y1), y2)))) MARK(cons(length(and(tt, y0)), z1)) -> c10(MARK(length(and(tt, y0)))) MARK(cons(length(and(s(y0), y1)), z1)) -> c10(MARK(length(and(s(y0), y1)))) MARK(cons(length(and(y0, y1)), z1)) -> c10(MARK(length(and(y0, y1)))) MARK(cons(length(and(zeros, y0)), z1)) -> c10(MARK(length(and(zeros, y0)))) MARK(cons(length(length(zeros)), z1)) -> c10(MARK(length(length(zeros)))) MARK(cons(length(length(and(y0, y1))), z1)) -> c10(MARK(length(length(and(y0, y1))))) MARK(cons(length(length(length(y0))), z1)) -> c10(MARK(length(length(length(y0))))) MARK(cons(length(length(cons(y0, y1))), z1)) -> c10(MARK(length(length(cons(y0, y1))))) MARK(cons(length(length(s(y0))), z1)) -> c10(MARK(length(length(s(y0))))) MARK(cons(length(length(y0)), z1)) -> c10(MARK(length(length(y0)))) MARK(cons(length(zeros), z1)) -> c10(MARK(length(zeros))) MARK(s(s(y0))) -> c14(MARK(s(y0))) MARK(s(and(cons(y0, y1), y2))) -> c14(MARK(and(cons(y0, y1), y2))) MARK(s(and(tt, y0))) -> c14(MARK(and(tt, y0))) MARK(s(and(s(y0), y1))) -> c14(MARK(and(s(y0), y1))) MARK(s(length(cons(y0, y1)))) -> c14(MARK(length(cons(y0, y1)))) MARK(s(length(s(y0)))) -> c14(MARK(length(s(y0)))) MARK(s(and(and(and(y0, y1), y2), y3))) -> c14(MARK(and(and(and(y0, y1), y2), y3))) MARK(s(and(and(length(y0), y1), y2))) -> c14(MARK(and(and(length(y0), y1), y2))) MARK(s(and(and(cons(y0, y1), y2), y3))) -> c14(MARK(and(and(cons(y0, y1), y2), y3))) MARK(s(and(and(tt, y0), y1))) -> c14(MARK(and(and(tt, y0), y1))) MARK(s(and(and(s(y0), y1), y2))) -> 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MARK(s(cons(and(length(cons(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(cons(y0, y1)), y2), y3))) MARK(s(cons(and(length(s(y0)), y1), y2))) -> c14(MARK(cons(and(length(s(y0)), y1), y2))) MARK(s(cons(and(length(y0), y1), y2))) -> c14(MARK(cons(and(length(y0), y1), y2))) MARK(s(cons(and(and(zeros, y0), y1), y2))) -> c14(MARK(cons(and(and(zeros, y0), y1), y2))) MARK(s(cons(length(and(and(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(and(y0, y1), y2)), y3))) MARK(s(cons(length(and(length(y0), y1)), y2))) -> c14(MARK(cons(length(and(length(y0), y1)), y2))) MARK(s(cons(length(and(cons(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(cons(y0, y1), y2)), y3))) MARK(s(cons(length(and(tt, y0)), y1))) -> c14(MARK(cons(length(and(tt, y0)), y1))) MARK(s(cons(length(and(s(y0), y1)), y2))) -> c14(MARK(cons(length(and(s(y0), y1)), y2))) MARK(s(cons(length(and(y0, y1)), y2))) -> c14(MARK(cons(length(and(y0, y1)), y2))) MARK(s(cons(length(and(zeros, y0)), y1))) -> c14(MARK(cons(length(and(zeros, 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A__LENGTH(cons(z0, s(length(s(y0))))) -> c5(MARK(s(length(s(y0))))) A__LENGTH(cons(z0, s(and(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(length(y0), y1), y2)))) -> c5(MARK(s(and(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(tt, y0), y1)))) -> c5(MARK(s(and(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(and(and(s(y0), y1), y2)))) -> c5(MARK(s(and(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(y0, y1), y2)))) -> c5(MARK(s(and(and(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(length(zeros), y0)))) -> c5(MARK(s(and(length(zeros), y0)))) A__LENGTH(cons(z0, s(and(length(and(y0, y1)), y2)))) -> c5(MARK(s(and(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(length(y0)), y1)))) -> c5(MARK(s(and(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(cons(y0, y1)), y2)))) -> c5(MARK(s(and(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(s(y0)), y1)))) -> c5(MARK(s(and(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(y0), y1)))) -> c5(MARK(s(and(length(y0), y1)))) A__LENGTH(cons(z0, s(and(and(zeros, y0), y1)))) -> c5(MARK(s(and(and(zeros, y0), y1)))) A__LENGTH(cons(z0, s(length(and(and(y0, y1), y2))))) -> c5(MARK(s(length(and(and(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(length(y0), y1))))) -> c5(MARK(s(length(and(length(y0), y1))))) A__LENGTH(cons(z0, s(length(and(cons(y0, y1), y2))))) -> c5(MARK(s(length(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(tt, y0))))) -> c5(MARK(s(length(and(tt, y0))))) A__LENGTH(cons(z0, s(length(and(s(y0), y1))))) -> c5(MARK(s(length(and(s(y0), y1))))) A__LENGTH(cons(z0, s(length(and(y0, y1))))) -> c5(MARK(s(length(and(y0, y1))))) A__LENGTH(cons(z0, s(length(and(zeros, y0))))) -> c5(MARK(s(length(and(zeros, y0))))) A__LENGTH(cons(z0, s(length(length(zeros))))) -> c5(MARK(s(length(length(zeros))))) A__LENGTH(cons(z0, s(length(length(and(y0, y1)))))) -> c5(MARK(s(length(length(and(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(length(y0)))))) -> c5(MARK(s(length(length(length(y0)))))) A__LENGTH(cons(z0, s(length(length(cons(y0, y1)))))) -> c5(MARK(s(length(length(cons(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(s(y0)))))) -> c5(MARK(s(length(length(s(y0)))))) A__LENGTH(cons(z0, s(length(length(y0))))) -> c5(MARK(s(length(length(y0))))) A__LENGTH(cons(z0, s(length(zeros)))) -> c5(MARK(s(length(zeros)))) A__LENGTH(cons(z0, s(cons(cons(y0, y1), y2)))) -> c5(MARK(s(cons(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(cons(s(y0), y1)))) -> c5(MARK(s(cons(s(y0), y1)))) A__LENGTH(cons(z0, s(cons(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(tt, y0), y1)))) -> c5(MARK(s(cons(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(cons(and(s(y0), y1), y2)))) -> c5(MARK(s(cons(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(length(cons(y0, y1)), y2)))) -> c5(MARK(s(cons(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(s(y0)), y1)))) -> c5(MARK(s(cons(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(cons(and(and(and(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(and(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(length(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(length(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(cons(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(tt, y0), y1), y2)))) -> c5(MARK(s(cons(and(and(tt, y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(and(s(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(s(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(zeros), y0), y1)))) -> c5(MARK(s(cons(and(length(zeros), y0), y1)))) A__LENGTH(cons(z0, s(cons(and(length(and(y0, y1)), y2), y3)))) -> c5(MARK(s(cons(and(length(and(y0, y1)), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(length(y0)), y1), y2)))) -> c5(MARK(s(cons(and(length(length(y0)), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(length(cons(y0, y1)), y2), y3)))) -> c5(MARK(s(cons(and(length(cons(y0, y1)), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(s(y0)), y1), y2)))) -> c5(MARK(s(cons(and(length(s(y0)), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(length(y0), y1), y2)))) -> c5(MARK(s(cons(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(and(zeros, y0), y1), y2)))) -> c5(MARK(s(cons(and(and(zeros, y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(length(and(and(y0, y1), y2)), y3)))) -> c5(MARK(s(cons(length(and(and(y0, y1), y2)), y3)))) A__LENGTH(cons(z0, s(cons(length(and(length(y0), y1)), y2)))) -> c5(MARK(s(cons(length(and(length(y0), y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(cons(y0, y1), y2)), y3)))) -> c5(MARK(s(cons(length(and(cons(y0, y1), y2)), y3)))) A__LENGTH(cons(z0, s(cons(length(and(tt, y0)), y1)))) -> c5(MARK(s(cons(length(and(tt, y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(and(s(y0), y1)), y2)))) -> c5(MARK(s(cons(length(and(s(y0), y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(y0, y1)), y2)))) -> c5(MARK(s(cons(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(zeros, y0)), y1)))) -> c5(MARK(s(cons(length(and(zeros, y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(length(zeros)), y0)))) -> c5(MARK(s(cons(length(length(zeros)), y0)))) A__LENGTH(cons(z0, s(cons(length(length(and(y0, y1))), y2)))) -> c5(MARK(s(cons(length(length(and(y0, y1))), y2)))) A__LENGTH(cons(z0, s(cons(length(length(length(y0))), y1)))) -> c5(MARK(s(cons(length(length(length(y0))), y1)))) A__LENGTH(cons(z0, s(cons(length(length(cons(y0, y1))), y2)))) -> c5(MARK(s(cons(length(length(cons(y0, y1))), y2)))) A__LENGTH(cons(z0, s(cons(length(length(s(y0))), y1)))) -> c5(MARK(s(cons(length(length(s(y0))), y1)))) A__LENGTH(cons(z0, s(cons(length(length(y0)), y1)))) -> c5(MARK(s(cons(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(zeros), y0)))) -> c5(MARK(s(cons(length(zeros), y0)))) MARK(and(cons(cons(y0, y1), z1), z2)) -> c8(MARK(cons(cons(y0, y1), z1))) MARK(and(cons(s(y0), z1), z2)) -> c8(MARK(cons(s(y0), z1))) MARK(and(cons(and(cons(y0, y1), y2), z1), z2)) -> c8(MARK(cons(and(cons(y0, y1), y2), z1))) MARK(and(cons(and(tt, y0), z1), z2)) -> c8(MARK(cons(and(tt, y0), z1))) MARK(and(cons(and(s(y0), y1), z1), z2)) -> c8(MARK(cons(and(s(y0), y1), z1))) MARK(and(cons(length(cons(y0, y1)), z1), z2)) -> c8(MARK(cons(length(cons(y0, y1)), z1))) MARK(and(cons(length(s(y0)), z1), z2)) -> c8(MARK(cons(length(s(y0)), z1))) MARK(and(cons(and(and(and(y0, y1), y2), y3), z1), z2)) -> c8(MARK(cons(and(and(and(y0, y1), y2), y3), z1))) MARK(and(cons(and(and(length(y0), y1), y2), z1), z2)) -> c8(MARK(cons(and(and(length(y0), y1), y2), z1))) MARK(and(cons(and(and(cons(y0, y1), y2), y3), z1), z2)) -> c8(MARK(cons(and(and(cons(y0, y1), y2), y3), z1))) MARK(and(cons(and(and(tt, y0), y1), z1), z2)) -> c8(MARK(cons(and(and(tt, y0), y1), z1))) MARK(and(cons(and(and(s(y0), y1), y2), z1), z2)) -> c8(MARK(cons(and(and(s(y0), y1), y2), z1))) MARK(and(cons(and(and(y0, y1), y2), z1), z2)) -> c8(MARK(cons(and(and(y0, y1), y2), z1))) MARK(and(cons(and(length(zeros), y0), z1), z2)) -> c8(MARK(cons(and(length(zeros), y0), z1))) MARK(and(cons(and(length(and(y0, y1)), y2), z1), z2)) -> c8(MARK(cons(and(length(and(y0, y1)), y2), z1))) MARK(and(cons(and(length(length(y0)), y1), z1), z2)) -> c8(MARK(cons(and(length(length(y0)), y1), z1))) MARK(and(cons(and(length(cons(y0, y1)), y2), z1), z2)) -> c8(MARK(cons(and(length(cons(y0, y1)), y2), z1))) MARK(and(cons(and(length(s(y0)), y1), z1), z2)) -> c8(MARK(cons(and(length(s(y0)), y1), z1))) MARK(and(cons(and(length(y0), y1), z1), z2)) -> c8(MARK(cons(and(length(y0), y1), z1))) MARK(and(cons(and(and(zeros, y0), y1), z1), z2)) -> c8(MARK(cons(and(and(zeros, y0), y1), z1))) MARK(and(cons(length(and(and(y0, y1), y2)), z1), z2)) -> c8(MARK(cons(length(and(and(y0, y1), y2)), z1))) MARK(and(cons(length(and(length(y0), y1)), z1), z2)) -> c8(MARK(cons(length(and(length(y0), y1)), z1))) MARK(and(cons(length(and(cons(y0, y1), y2)), z1), z2)) -> c8(MARK(cons(length(and(cons(y0, y1), y2)), z1))) MARK(and(cons(length(and(tt, y0)), z1), z2)) -> c8(MARK(cons(length(and(tt, y0)), z1))) MARK(and(cons(length(and(s(y0), y1)), z1), z2)) -> c8(MARK(cons(length(and(s(y0), y1)), z1))) MARK(and(cons(length(and(y0, y1)), z1), z2)) -> c8(MARK(cons(length(and(y0, y1)), z1))) MARK(and(cons(length(and(zeros, y0)), z1), z2)) -> c8(MARK(cons(length(and(zeros, y0)), z1))) MARK(and(cons(length(length(zeros)), z1), z2)) -> c8(MARK(cons(length(length(zeros)), z1))) MARK(and(cons(length(length(and(y0, y1))), z1), z2)) -> c8(MARK(cons(length(length(and(y0, y1))), z1))) MARK(and(cons(length(length(length(y0))), z1), z2)) -> c8(MARK(cons(length(length(length(y0))), z1))) MARK(and(cons(length(length(cons(y0, y1))), z1), z2)) -> c8(MARK(cons(length(length(cons(y0, y1))), z1))) MARK(and(cons(length(length(s(y0))), z1), z2)) -> c8(MARK(cons(length(length(s(y0))), z1))) MARK(and(cons(length(length(y0)), z1), z2)) -> c8(MARK(cons(length(length(y0)), z1))) MARK(and(cons(length(zeros), z1), z2)) -> c8(MARK(cons(length(zeros), z1))) MARK(and(tt, cons(y0, y1))) -> c8(A__AND(tt, cons(y0, y1))) MARK(and(tt, s(y0))) -> c8(A__AND(tt, s(y0))) MARK(and(tt, and(cons(y0, y1), y2))) -> c8(A__AND(tt, and(cons(y0, y1), y2))) MARK(and(tt, and(tt, y0))) -> c8(A__AND(tt, and(tt, y0))) MARK(and(tt, and(s(y0), y1))) -> c8(A__AND(tt, and(s(y0), y1))) MARK(and(tt, length(cons(y0, y1)))) -> c8(A__AND(tt, length(cons(y0, y1)))) MARK(and(tt, length(s(y0)))) -> c8(A__AND(tt, length(s(y0)))) MARK(and(tt, and(and(and(y0, y1), y2), y3))) -> c8(A__AND(tt, and(and(and(y0, y1), y2), y3))) MARK(and(tt, and(and(length(y0), y1), y2))) -> c8(A__AND(tt, and(and(length(y0), y1), y2))) MARK(and(tt, and(and(cons(y0, y1), y2), y3))) -> c8(A__AND(tt, and(and(cons(y0, y1), y2), y3))) MARK(and(tt, and(and(tt, y0), y1))) -> c8(A__AND(tt, and(and(tt, y0), y1))) MARK(and(tt, and(and(s(y0), y1), y2))) -> c8(A__AND(tt, and(and(s(y0), y1), y2))) MARK(and(tt, and(and(y0, y1), y2))) -> c8(A__AND(tt, and(and(y0, y1), y2))) MARK(and(tt, and(length(zeros), y0))) -> c8(A__AND(tt, and(length(zeros), y0))) MARK(and(tt, and(length(and(y0, y1)), y2))) -> c8(A__AND(tt, and(length(and(y0, y1)), y2))) MARK(and(tt, and(length(length(y0)), y1))) -> c8(A__AND(tt, and(length(length(y0)), y1))) MARK(and(tt, and(length(cons(y0, y1)), y2))) -> c8(A__AND(tt, and(length(cons(y0, y1)), y2))) MARK(and(tt, and(length(s(y0)), y1))) -> c8(A__AND(tt, and(length(s(y0)), y1))) MARK(and(tt, and(length(y0), y1))) -> c8(A__AND(tt, and(length(y0), y1))) MARK(and(tt, and(and(zeros, y0), y1))) -> c8(A__AND(tt, and(and(zeros, y0), y1))) MARK(and(tt, length(and(and(y0, y1), y2)))) -> c8(A__AND(tt, length(and(and(y0, y1), y2)))) MARK(and(tt, length(and(length(y0), y1)))) -> c8(A__AND(tt, length(and(length(y0), y1)))) MARK(and(tt, length(and(cons(y0, y1), y2)))) -> c8(A__AND(tt, length(and(cons(y0, y1), y2)))) MARK(and(tt, length(and(tt, y0)))) -> c8(A__AND(tt, length(and(tt, y0)))) MARK(and(tt, length(and(s(y0), y1)))) -> c8(A__AND(tt, length(and(s(y0), y1)))) MARK(and(tt, length(and(y0, y1)))) -> c8(A__AND(tt, length(and(y0, y1)))) MARK(and(tt, length(and(zeros, y0)))) -> c8(A__AND(tt, length(and(zeros, y0)))) MARK(and(tt, length(length(zeros)))) -> c8(A__AND(tt, length(length(zeros)))) MARK(and(tt, length(length(and(y0, y1))))) -> c8(A__AND(tt, length(length(and(y0, y1))))) MARK(and(tt, length(length(length(y0))))) -> c8(A__AND(tt, length(length(length(y0))))) MARK(and(tt, length(length(cons(y0, y1))))) -> c8(A__AND(tt, length(length(cons(y0, y1))))) MARK(and(tt, length(length(s(y0))))) -> c8(A__AND(tt, length(length(s(y0))))) MARK(and(tt, length(length(y0)))) -> c8(A__AND(tt, length(length(y0)))) MARK(and(tt, length(zeros))) -> c8(A__AND(tt, length(zeros))) MARK(and(s(s(y0)), z1)) -> c8(MARK(s(s(y0)))) MARK(and(s(and(cons(y0, y1), y2)), z1)) -> c8(MARK(s(and(cons(y0, y1), y2)))) MARK(and(s(and(tt, y0)), z1)) -> c8(MARK(s(and(tt, y0)))) MARK(and(s(and(s(y0), y1)), z1)) -> c8(MARK(s(and(s(y0), y1)))) MARK(and(s(length(cons(y0, y1))), z1)) -> c8(MARK(s(length(cons(y0, y1))))) MARK(and(s(length(s(y0))), z1)) -> c8(MARK(s(length(s(y0))))) MARK(and(s(and(and(and(y0, y1), y2), y3)), z1)) -> c8(MARK(s(and(and(and(y0, y1), y2), y3)))) MARK(and(s(and(and(length(y0), y1), y2)), z1)) -> c8(MARK(s(and(and(length(y0), y1), y2)))) MARK(and(s(and(and(cons(y0, y1), y2), y3)), z1)) -> c8(MARK(s(and(and(cons(y0, y1), y2), y3)))) MARK(and(s(and(and(tt, y0), y1)), z1)) -> c8(MARK(s(and(and(tt, y0), y1)))) MARK(and(s(and(and(s(y0), y1), y2)), z1)) -> c8(MARK(s(and(and(s(y0), y1), y2)))) MARK(and(s(and(and(y0, y1), y2)), z1)) -> c8(MARK(s(and(and(y0, y1), y2)))) MARK(and(s(and(length(zeros), y0)), z1)) -> c8(MARK(s(and(length(zeros), y0)))) MARK(and(s(and(length(and(y0, y1)), y2)), z1)) -> c8(MARK(s(and(length(and(y0, y1)), y2)))) MARK(and(s(and(length(length(y0)), y1)), z1)) -> c8(MARK(s(and(length(length(y0)), y1)))) MARK(and(s(and(length(cons(y0, y1)), y2)), z1)) -> c8(MARK(s(and(length(cons(y0, y1)), y2)))) MARK(and(s(and(length(s(y0)), y1)), z1)) -> c8(MARK(s(and(length(s(y0)), y1)))) MARK(and(s(and(length(y0), y1)), z1)) -> c8(MARK(s(and(length(y0), y1)))) MARK(and(s(and(and(zeros, y0), y1)), z1)) -> c8(MARK(s(and(and(zeros, y0), y1)))) MARK(and(s(length(and(and(y0, y1), y2))), z1)) -> c8(MARK(s(length(and(and(y0, y1), y2))))) MARK(and(s(length(and(length(y0), y1))), z1)) -> c8(MARK(s(length(and(length(y0), y1))))) MARK(and(s(length(and(cons(y0, y1), y2))), z1)) -> c8(MARK(s(length(and(cons(y0, y1), y2))))) MARK(and(s(length(and(tt, y0))), z1)) -> c8(MARK(s(length(and(tt, y0))))) MARK(and(s(length(and(s(y0), y1))), z1)) -> c8(MARK(s(length(and(s(y0), y1))))) MARK(and(s(length(and(y0, y1))), z1)) -> c8(MARK(s(length(and(y0, y1))))) MARK(and(s(length(and(zeros, y0))), z1)) -> c8(MARK(s(length(and(zeros, y0))))) MARK(and(s(length(length(zeros))), z1)) -> c8(MARK(s(length(length(zeros))))) MARK(and(s(length(length(and(y0, y1)))), z1)) -> c8(MARK(s(length(length(and(y0, y1)))))) MARK(and(s(length(length(length(y0)))), z1)) -> c8(MARK(s(length(length(length(y0)))))) MARK(and(s(length(length(cons(y0, y1)))), z1)) -> c8(MARK(s(length(length(cons(y0, y1)))))) MARK(and(s(length(length(s(y0)))), z1)) -> c8(MARK(s(length(length(s(y0)))))) MARK(and(s(length(length(y0))), z1)) -> c8(MARK(s(length(length(y0))))) MARK(and(s(length(zeros)), z1)) -> c8(MARK(s(length(zeros)))) MARK(and(s(cons(cons(y0, y1), y2)), z1)) -> c8(MARK(s(cons(cons(y0, y1), y2)))) MARK(and(s(cons(s(y0), y1)), z1)) -> c8(MARK(s(cons(s(y0), y1)))) MARK(and(s(cons(and(cons(y0, y1), y2), y3)), z1)) -> c8(MARK(s(cons(and(cons(y0, y1), y2), y3)))) MARK(and(s(cons(and(tt, y0), y1)), z1)) -> c8(MARK(s(cons(and(tt, y0), y1)))) MARK(and(s(cons(and(s(y0), y1), y2)), z1)) -> c8(MARK(s(cons(and(s(y0), y1), y2)))) MARK(and(s(cons(length(cons(y0, y1)), y2)), z1)) -> c8(MARK(s(cons(length(cons(y0, y1)), y2)))) MARK(and(s(cons(length(s(y0)), y1)), z1)) -> c8(MARK(s(cons(length(s(y0)), y1)))) MARK(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), z1)) -> c8(MARK(s(cons(and(and(and(y0, y1), y2), y3), y4)))) MARK(and(s(cons(and(and(length(y0), y1), y2), y3)), z1)) -> c8(MARK(s(cons(and(and(length(y0), y1), y2), y3)))) MARK(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), z1)) -> c8(MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) MARK(and(s(cons(and(and(tt, y0), y1), y2)), z1)) -> c8(MARK(s(cons(and(and(tt, y0), y1), y2)))) MARK(and(s(cons(and(and(s(y0), y1), y2), y3)), z1)) -> c8(MARK(s(cons(and(and(s(y0), y1), y2), y3)))) MARK(and(s(cons(and(and(y0, y1), y2), y3)), z1)) -> c8(MARK(s(cons(and(and(y0, y1), y2), y3)))) MARK(and(s(cons(and(length(zeros), y0), y1)), z1)) -> c8(MARK(s(cons(and(length(zeros), y0), y1)))) MARK(and(s(cons(and(length(and(y0, y1)), y2), y3)), z1)) -> c8(MARK(s(cons(and(length(and(y0, y1)), y2), y3)))) MARK(and(s(cons(and(length(length(y0)), y1), y2)), z1)) -> c8(MARK(s(cons(and(length(length(y0)), y1), y2)))) MARK(and(s(cons(and(length(cons(y0, y1)), y2), y3)), z1)) -> c8(MARK(s(cons(and(length(cons(y0, y1)), y2), y3)))) MARK(and(s(cons(and(length(s(y0)), y1), y2)), z1)) -> c8(MARK(s(cons(and(length(s(y0)), y1), y2)))) MARK(and(s(cons(and(length(y0), y1), y2)), z1)) -> c8(MARK(s(cons(and(length(y0), y1), y2)))) MARK(and(s(cons(and(and(zeros, y0), y1), y2)), z1)) -> c8(MARK(s(cons(and(and(zeros, y0), y1), y2)))) MARK(and(s(cons(length(and(and(y0, y1), y2)), y3)), z1)) -> c8(MARK(s(cons(length(and(and(y0, y1), y2)), y3)))) MARK(and(s(cons(length(and(length(y0), y1)), y2)), z1)) -> c8(MARK(s(cons(length(and(length(y0), y1)), y2)))) MARK(and(s(cons(length(and(cons(y0, y1), y2)), y3)), z1)) -> c8(MARK(s(cons(length(and(cons(y0, y1), y2)), y3)))) MARK(and(s(cons(length(and(tt, y0)), y1)), z1)) -> c8(MARK(s(cons(length(and(tt, y0)), y1)))) MARK(and(s(cons(length(and(s(y0), y1)), y2)), z1)) -> c8(MARK(s(cons(length(and(s(y0), y1)), y2)))) MARK(and(s(cons(length(and(y0, y1)), y2)), z1)) -> c8(MARK(s(cons(length(and(y0, y1)), y2)))) MARK(and(s(cons(length(and(zeros, y0)), y1)), z1)) -> c8(MARK(s(cons(length(and(zeros, y0)), y1)))) MARK(and(s(cons(length(length(zeros)), y0)), z1)) -> c8(MARK(s(cons(length(length(zeros)), y0)))) MARK(and(s(cons(length(length(and(y0, y1))), y2)), z1)) -> c8(MARK(s(cons(length(length(and(y0, y1))), y2)))) MARK(and(s(cons(length(length(length(y0))), y1)), z1)) -> c8(MARK(s(cons(length(length(length(y0))), y1)))) MARK(and(s(cons(length(length(cons(y0, y1))), y2)), z1)) -> c8(MARK(s(cons(length(length(cons(y0, y1))), y2)))) MARK(and(s(cons(length(length(s(y0))), y1)), z1)) -> c8(MARK(s(cons(length(length(s(y0))), y1)))) MARK(and(s(cons(length(length(y0)), y1)), z1)) -> c8(MARK(s(cons(length(length(y0)), y1)))) MARK(and(s(cons(length(zeros), y0)), z1)) -> c8(MARK(s(cons(length(zeros), y0)))) MARK(length(s(s(y0)))) -> c9(MARK(s(s(y0)))) MARK(length(s(and(cons(y0, y1), y2)))) -> c9(MARK(s(and(cons(y0, y1), y2)))) MARK(length(s(and(tt, y0)))) -> c9(MARK(s(and(tt, y0)))) MARK(length(s(and(s(y0), y1)))) -> c9(MARK(s(and(s(y0), y1)))) MARK(length(s(length(cons(y0, y1))))) -> c9(MARK(s(length(cons(y0, y1))))) MARK(length(s(length(s(y0))))) -> c9(MARK(s(length(s(y0))))) MARK(length(s(and(and(and(y0, y1), y2), y3)))) -> c9(MARK(s(and(and(and(y0, y1), y2), y3)))) MARK(length(s(and(and(length(y0), y1), y2)))) -> c9(MARK(s(and(and(length(y0), y1), y2)))) MARK(length(s(and(and(cons(y0, y1), y2), y3)))) -> c9(MARK(s(and(and(cons(y0, y1), y2), y3)))) MARK(length(s(and(and(tt, y0), y1)))) -> c9(MARK(s(and(and(tt, y0), y1)))) MARK(length(s(and(and(s(y0), y1), y2)))) -> c9(MARK(s(and(and(s(y0), y1), y2)))) MARK(length(s(and(and(y0, y1), y2)))) -> c9(MARK(s(and(and(y0, y1), y2)))) MARK(length(s(and(length(zeros), y0)))) -> c9(MARK(s(and(length(zeros), y0)))) MARK(length(s(and(length(and(y0, y1)), y2)))) -> c9(MARK(s(and(length(and(y0, y1)), y2)))) MARK(length(s(and(length(length(y0)), y1)))) -> c9(MARK(s(and(length(length(y0)), y1)))) MARK(length(s(and(length(cons(y0, y1)), y2)))) -> c9(MARK(s(and(length(cons(y0, y1)), y2)))) MARK(length(s(and(length(s(y0)), y1)))) -> c9(MARK(s(and(length(s(y0)), y1)))) MARK(length(s(and(length(y0), y1)))) -> c9(MARK(s(and(length(y0), y1)))) MARK(length(s(and(and(zeros, y0), y1)))) -> c9(MARK(s(and(and(zeros, y0), y1)))) MARK(length(s(length(and(and(y0, y1), y2))))) -> c9(MARK(s(length(and(and(y0, y1), y2))))) MARK(length(s(length(and(length(y0), y1))))) -> c9(MARK(s(length(and(length(y0), y1))))) MARK(length(s(length(and(cons(y0, y1), y2))))) -> c9(MARK(s(length(and(cons(y0, y1), y2))))) MARK(length(s(length(and(tt, y0))))) -> c9(MARK(s(length(and(tt, y0))))) MARK(length(s(length(and(s(y0), y1))))) -> c9(MARK(s(length(and(s(y0), y1))))) MARK(length(s(length(and(y0, y1))))) -> c9(MARK(s(length(and(y0, y1))))) MARK(length(s(length(and(zeros, y0))))) -> c9(MARK(s(length(and(zeros, y0))))) MARK(length(s(length(length(zeros))))) -> c9(MARK(s(length(length(zeros))))) MARK(length(s(length(length(and(y0, y1)))))) -> c9(MARK(s(length(length(and(y0, y1)))))) MARK(length(s(length(length(length(y0)))))) -> c9(MARK(s(length(length(length(y0)))))) MARK(length(s(length(length(cons(y0, y1)))))) -> c9(MARK(s(length(length(cons(y0, y1)))))) MARK(length(s(length(length(s(y0)))))) -> c9(MARK(s(length(length(s(y0)))))) MARK(length(s(length(length(y0))))) -> c9(MARK(s(length(length(y0))))) MARK(length(s(length(zeros)))) -> c9(MARK(s(length(zeros)))) MARK(length(s(cons(cons(y0, y1), y2)))) -> c9(MARK(s(cons(cons(y0, y1), y2)))) MARK(length(s(cons(s(y0), y1)))) -> c9(MARK(s(cons(s(y0), y1)))) MARK(length(s(cons(and(cons(y0, y1), y2), y3)))) -> c9(MARK(s(cons(and(cons(y0, y1), y2), y3)))) MARK(length(s(cons(and(tt, y0), y1)))) -> c9(MARK(s(cons(and(tt, y0), y1)))) MARK(length(s(cons(and(s(y0), y1), y2)))) -> c9(MARK(s(cons(and(s(y0), y1), y2)))) MARK(length(s(cons(length(cons(y0, y1)), y2)))) -> c9(MARK(s(cons(length(cons(y0, y1)), y2)))) MARK(length(s(cons(length(s(y0)), y1)))) -> c9(MARK(s(cons(length(s(y0)), y1)))) MARK(length(s(cons(and(and(and(y0, y1), y2), y3), y4)))) -> c9(MARK(s(cons(and(and(and(y0, y1), y2), y3), y4)))) MARK(length(s(cons(and(and(length(y0), y1), y2), y3)))) -> c9(MARK(s(cons(and(and(length(y0), y1), y2), y3)))) MARK(length(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) -> c9(MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) MARK(length(s(cons(and(and(tt, y0), y1), y2)))) -> c9(MARK(s(cons(and(and(tt, y0), y1), y2)))) MARK(length(s(cons(and(and(s(y0), y1), y2), y3)))) -> c9(MARK(s(cons(and(and(s(y0), y1), y2), y3)))) MARK(length(s(cons(and(and(y0, y1), y2), y3)))) -> c9(MARK(s(cons(and(and(y0, y1), y2), y3)))) MARK(length(s(cons(and(length(zeros), y0), y1)))) -> c9(MARK(s(cons(and(length(zeros), y0), y1)))) MARK(length(s(cons(and(length(and(y0, y1)), y2), y3)))) -> c9(MARK(s(cons(and(length(and(y0, y1)), y2), y3)))) MARK(length(s(cons(and(length(length(y0)), y1), y2)))) -> c9(MARK(s(cons(and(length(length(y0)), y1), y2)))) MARK(length(s(cons(and(length(cons(y0, y1)), y2), y3)))) -> c9(MARK(s(cons(and(length(cons(y0, y1)), y2), y3)))) MARK(length(s(cons(and(length(s(y0)), y1), y2)))) -> c9(MARK(s(cons(and(length(s(y0)), y1), y2)))) MARK(length(s(cons(and(length(y0), y1), y2)))) -> c9(MARK(s(cons(and(length(y0), y1), y2)))) MARK(length(s(cons(and(and(zeros, y0), y1), y2)))) -> c9(MARK(s(cons(and(and(zeros, y0), y1), y2)))) MARK(length(s(cons(length(and(and(y0, y1), y2)), y3)))) -> c9(MARK(s(cons(length(and(and(y0, y1), y2)), y3)))) MARK(length(s(cons(length(and(length(y0), y1)), y2)))) -> c9(MARK(s(cons(length(and(length(y0), y1)), y2)))) MARK(length(s(cons(length(and(cons(y0, y1), y2)), y3)))) -> c9(MARK(s(cons(length(and(cons(y0, y1), y2)), y3)))) MARK(length(s(cons(length(and(tt, y0)), y1)))) -> c9(MARK(s(cons(length(and(tt, y0)), y1)))) MARK(length(s(cons(length(and(s(y0), y1)), y2)))) -> c9(MARK(s(cons(length(and(s(y0), y1)), y2)))) MARK(length(s(cons(length(and(y0, y1)), y2)))) -> c9(MARK(s(cons(length(and(y0, y1)), y2)))) MARK(length(s(cons(length(and(zeros, y0)), y1)))) -> c9(MARK(s(cons(length(and(zeros, y0)), y1)))) MARK(length(s(cons(length(length(zeros)), y0)))) -> c9(MARK(s(cons(length(length(zeros)), y0)))) MARK(length(s(cons(length(length(and(y0, y1))), y2)))) -> c9(MARK(s(cons(length(length(and(y0, y1))), y2)))) MARK(length(s(cons(length(length(length(y0))), y1)))) -> c9(MARK(s(cons(length(length(length(y0))), y1)))) MARK(length(s(cons(length(length(cons(y0, y1))), y2)))) -> c9(MARK(s(cons(length(length(cons(y0, y1))), y2)))) MARK(length(s(cons(length(length(s(y0))), y1)))) -> c9(MARK(s(cons(length(length(s(y0))), y1)))) MARK(length(s(cons(length(length(y0)), y1)))) -> c9(MARK(s(cons(length(length(y0)), y1)))) MARK(length(s(cons(length(zeros), y0)))) -> c9(MARK(s(cons(length(zeros), y0)))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__LENGTH_1, MARK_1, A__AND_2 Compound Symbols: c5_2, c9_2, c5_1, c8_2, c8_1, c9_1, c2_1, c10_1, c14_1 ---------------------------------------- (181) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) by A__LENGTH(cons(z0, and(and(and(y0, y1), y2), z2))) -> c5(MARK(and(and(and(y0, y1), y2), z2))) A__LENGTH(cons(z0, and(and(length(y0), y1), z2))) -> c5(MARK(and(and(length(y0), y1), z2))) A__LENGTH(cons(z0, and(and(cons(y0, y1), y2), z2))) -> c5(MARK(and(and(cons(y0, y1), y2), z2))) A__LENGTH(cons(z0, and(and(tt, y0), z2))) -> c5(MARK(and(and(tt, y0), z2))) A__LENGTH(cons(z0, and(and(s(y0), y1), z2))) -> c5(MARK(and(and(s(y0), y1), z2))) A__LENGTH(cons(z0, and(and(y0, y1), z2))) -> c5(MARK(and(and(y0, y1), z2))) A__LENGTH(cons(z0, and(length(zeros), z2))) -> c5(MARK(and(length(zeros), z2))) A__LENGTH(cons(z0, and(length(and(y0, y1)), z2))) -> c5(MARK(and(length(and(y0, y1)), z2))) A__LENGTH(cons(z0, and(length(length(y0)), z2))) -> c5(MARK(and(length(length(y0)), z2))) A__LENGTH(cons(z0, and(length(cons(y0, y1)), z2))) -> c5(MARK(and(length(cons(y0, y1)), z2))) A__LENGTH(cons(z0, and(length(s(y0)), z2))) -> c5(MARK(and(length(s(y0)), z2))) A__LENGTH(cons(z0, and(length(y0), z2))) -> c5(MARK(and(length(y0), z2))) A__LENGTH(cons(z0, and(and(zeros, y0), z2))) -> c5(MARK(and(and(zeros, y0), z2))) A__LENGTH(cons(z0, and(cons(cons(y0, y1), y2), z2))) -> c5(MARK(and(cons(cons(y0, y1), y2), z2))) A__LENGTH(cons(z0, and(cons(s(y0), y1), z2))) -> c5(MARK(and(cons(s(y0), y1), z2))) A__LENGTH(cons(z0, and(cons(and(cons(y0, y1), y2), y3), z2))) -> c5(MARK(and(cons(and(cons(y0, y1), y2), y3), z2))) A__LENGTH(cons(z0, and(cons(and(tt, y0), y1), z2))) -> c5(MARK(and(cons(and(tt, y0), y1), z2))) A__LENGTH(cons(z0, and(cons(and(s(y0), y1), y2), z2))) -> c5(MARK(and(cons(and(s(y0), y1), y2), z2))) A__LENGTH(cons(z0, and(cons(length(cons(y0, y1)), y2), z2))) -> c5(MARK(and(cons(length(cons(y0, y1)), y2), z2))) A__LENGTH(cons(z0, and(cons(length(s(y0)), y1), z2))) -> c5(MARK(and(cons(length(s(y0)), y1), z2))) A__LENGTH(cons(z0, and(cons(and(and(and(y0, y1), y2), y3), y4), z2))) -> c5(MARK(and(cons(and(and(and(y0, y1), y2), y3), y4), z2))) A__LENGTH(cons(z0, and(cons(and(and(length(y0), y1), y2), y3), z2))) -> c5(MARK(and(cons(and(and(length(y0), y1), y2), y3), z2))) A__LENGTH(cons(z0, and(cons(and(and(cons(y0, y1), y2), y3), y4), z2))) -> c5(MARK(and(cons(and(and(cons(y0, y1), y2), y3), y4), z2))) A__LENGTH(cons(z0, and(cons(and(and(tt, y0), y1), y2), z2))) -> c5(MARK(and(cons(and(and(tt, y0), y1), y2), z2))) A__LENGTH(cons(z0, and(cons(and(and(s(y0), y1), y2), y3), z2))) -> c5(MARK(and(cons(and(and(s(y0), y1), y2), y3), z2))) A__LENGTH(cons(z0, and(cons(and(and(y0, y1), y2), y3), z2))) -> c5(MARK(and(cons(and(and(y0, y1), y2), y3), z2))) A__LENGTH(cons(z0, and(cons(and(length(zeros), y0), y1), z2))) -> c5(MARK(and(cons(and(length(zeros), y0), y1), z2))) A__LENGTH(cons(z0, and(cons(and(length(and(y0, y1)), y2), y3), z2))) -> c5(MARK(and(cons(and(length(and(y0, y1)), y2), y3), z2))) A__LENGTH(cons(z0, and(cons(and(length(length(y0)), y1), y2), z2))) -> c5(MARK(and(cons(and(length(length(y0)), y1), y2), z2))) A__LENGTH(cons(z0, and(cons(and(length(cons(y0, y1)), y2), y3), z2))) -> c5(MARK(and(cons(and(length(cons(y0, y1)), y2), y3), z2))) A__LENGTH(cons(z0, and(cons(and(length(s(y0)), y1), y2), z2))) -> c5(MARK(and(cons(and(length(s(y0)), y1), y2), z2))) A__LENGTH(cons(z0, and(cons(and(length(y0), y1), y2), z2))) -> c5(MARK(and(cons(and(length(y0), y1), y2), z2))) A__LENGTH(cons(z0, and(cons(and(and(zeros, y0), y1), y2), z2))) -> c5(MARK(and(cons(and(and(zeros, y0), y1), y2), z2))) A__LENGTH(cons(z0, and(cons(length(and(and(y0, y1), y2)), y3), z2))) -> c5(MARK(and(cons(length(and(and(y0, y1), y2)), y3), z2))) A__LENGTH(cons(z0, and(cons(length(and(length(y0), y1)), y2), z2))) -> c5(MARK(and(cons(length(and(length(y0), y1)), y2), z2))) A__LENGTH(cons(z0, and(cons(length(and(cons(y0, y1), y2)), y3), z2))) -> c5(MARK(and(cons(length(and(cons(y0, y1), y2)), y3), z2))) A__LENGTH(cons(z0, and(cons(length(and(tt, y0)), y1), z2))) -> c5(MARK(and(cons(length(and(tt, y0)), y1), z2))) A__LENGTH(cons(z0, and(cons(length(and(s(y0), y1)), y2), z2))) -> c5(MARK(and(cons(length(and(s(y0), y1)), y2), z2))) A__LENGTH(cons(z0, and(cons(length(and(y0, y1)), y2), z2))) -> c5(MARK(and(cons(length(and(y0, y1)), y2), z2))) A__LENGTH(cons(z0, and(cons(length(and(zeros, y0)), y1), z2))) -> c5(MARK(and(cons(length(and(zeros, y0)), y1), z2))) A__LENGTH(cons(z0, and(cons(length(length(zeros)), y0), z2))) -> c5(MARK(and(cons(length(length(zeros)), y0), z2))) A__LENGTH(cons(z0, and(cons(length(length(and(y0, y1))), y2), z2))) -> c5(MARK(and(cons(length(length(and(y0, y1))), y2), z2))) A__LENGTH(cons(z0, and(cons(length(length(length(y0))), y1), z2))) -> c5(MARK(and(cons(length(length(length(y0))), y1), z2))) A__LENGTH(cons(z0, and(cons(length(length(cons(y0, y1))), y2), z2))) -> c5(MARK(and(cons(length(length(cons(y0, y1))), y2), z2))) A__LENGTH(cons(z0, and(cons(length(length(s(y0))), y1), z2))) -> c5(MARK(and(cons(length(length(s(y0))), y1), z2))) A__LENGTH(cons(z0, and(cons(length(length(y0)), y1), z2))) -> c5(MARK(and(cons(length(length(y0)), y1), z2))) A__LENGTH(cons(z0, and(cons(length(zeros), y0), z2))) -> c5(MARK(and(cons(length(zeros), y0), z2))) A__LENGTH(cons(z0, and(tt, cons(y0, y1)))) -> c5(MARK(and(tt, cons(y0, y1)))) A__LENGTH(cons(z0, and(tt, s(y0)))) -> c5(MARK(and(tt, s(y0)))) A__LENGTH(cons(z0, and(tt, and(cons(y0, y1), y2)))) -> c5(MARK(and(tt, and(cons(y0, y1), y2)))) A__LENGTH(cons(z0, and(tt, and(tt, y0)))) -> c5(MARK(and(tt, and(tt, y0)))) A__LENGTH(cons(z0, and(tt, and(s(y0), y1)))) -> c5(MARK(and(tt, and(s(y0), y1)))) A__LENGTH(cons(z0, and(tt, length(cons(y0, y1))))) -> c5(MARK(and(tt, length(cons(y0, y1))))) A__LENGTH(cons(z0, and(tt, length(s(y0))))) -> c5(MARK(and(tt, length(s(y0))))) A__LENGTH(cons(z0, and(tt, and(and(and(y0, y1), y2), y3)))) -> c5(MARK(and(tt, and(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, and(tt, and(and(length(y0), y1), y2)))) -> c5(MARK(and(tt, and(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, and(tt, and(and(cons(y0, y1), y2), y3)))) -> c5(MARK(and(tt, and(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, and(tt, and(and(tt, y0), y1)))) -> c5(MARK(and(tt, and(and(tt, y0), y1)))) A__LENGTH(cons(z0, and(tt, and(and(s(y0), y1), y2)))) -> c5(MARK(and(tt, and(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, and(tt, and(and(y0, y1), y2)))) -> c5(MARK(and(tt, and(and(y0, y1), y2)))) A__LENGTH(cons(z0, and(tt, and(length(zeros), y0)))) -> c5(MARK(and(tt, and(length(zeros), y0)))) A__LENGTH(cons(z0, and(tt, and(length(and(y0, y1)), y2)))) -> c5(MARK(and(tt, and(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, and(tt, and(length(length(y0)), y1)))) -> c5(MARK(and(tt, and(length(length(y0)), y1)))) A__LENGTH(cons(z0, and(tt, and(length(cons(y0, y1)), y2)))) -> c5(MARK(and(tt, and(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, and(tt, and(length(s(y0)), y1)))) -> c5(MARK(and(tt, and(length(s(y0)), y1)))) A__LENGTH(cons(z0, and(tt, and(length(y0), y1)))) -> c5(MARK(and(tt, and(length(y0), y1)))) A__LENGTH(cons(z0, and(tt, and(and(zeros, y0), y1)))) -> c5(MARK(and(tt, and(and(zeros, y0), y1)))) A__LENGTH(cons(z0, and(tt, length(and(and(y0, y1), y2))))) -> c5(MARK(and(tt, length(and(and(y0, y1), y2))))) A__LENGTH(cons(z0, and(tt, length(and(length(y0), y1))))) -> c5(MARK(and(tt, length(and(length(y0), y1))))) A__LENGTH(cons(z0, and(tt, length(and(cons(y0, y1), y2))))) -> c5(MARK(and(tt, length(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, and(tt, length(and(tt, y0))))) -> c5(MARK(and(tt, length(and(tt, y0))))) A__LENGTH(cons(z0, and(tt, length(and(s(y0), y1))))) -> c5(MARK(and(tt, length(and(s(y0), y1))))) A__LENGTH(cons(z0, and(tt, length(and(y0, y1))))) -> c5(MARK(and(tt, length(and(y0, y1))))) A__LENGTH(cons(z0, and(tt, length(and(zeros, y0))))) -> c5(MARK(and(tt, length(and(zeros, y0))))) A__LENGTH(cons(z0, and(tt, length(length(zeros))))) -> c5(MARK(and(tt, length(length(zeros))))) A__LENGTH(cons(z0, and(tt, length(length(and(y0, y1)))))) -> c5(MARK(and(tt, length(length(and(y0, y1)))))) A__LENGTH(cons(z0, and(tt, length(length(length(y0)))))) -> c5(MARK(and(tt, length(length(length(y0)))))) A__LENGTH(cons(z0, and(tt, length(length(cons(y0, y1)))))) -> c5(MARK(and(tt, length(length(cons(y0, y1)))))) A__LENGTH(cons(z0, and(tt, length(length(s(y0)))))) -> c5(MARK(and(tt, length(length(s(y0)))))) A__LENGTH(cons(z0, and(tt, length(length(y0))))) -> c5(MARK(and(tt, length(length(y0))))) A__LENGTH(cons(z0, and(tt, length(zeros)))) -> c5(MARK(and(tt, length(zeros)))) A__LENGTH(cons(z0, and(s(s(y0)), z2))) -> c5(MARK(and(s(s(y0)), z2))) A__LENGTH(cons(z0, and(s(and(cons(y0, y1), y2)), z2))) -> c5(MARK(and(s(and(cons(y0, y1), y2)), z2))) A__LENGTH(cons(z0, and(s(and(tt, y0)), z2))) -> c5(MARK(and(s(and(tt, y0)), z2))) A__LENGTH(cons(z0, and(s(and(s(y0), y1)), z2))) -> c5(MARK(and(s(and(s(y0), y1)), z2))) A__LENGTH(cons(z0, and(s(length(cons(y0, y1))), z2))) -> c5(MARK(and(s(length(cons(y0, y1))), z2))) A__LENGTH(cons(z0, and(s(length(s(y0))), z2))) -> c5(MARK(and(s(length(s(y0))), z2))) A__LENGTH(cons(z0, and(s(and(and(and(y0, y1), y2), y3)), z2))) -> c5(MARK(and(s(and(and(and(y0, y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(and(and(length(y0), y1), y2)), z2))) -> c5(MARK(and(s(and(and(length(y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(and(and(cons(y0, y1), y2), y3)), z2))) -> c5(MARK(and(s(and(and(cons(y0, y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(and(and(tt, y0), y1)), z2))) -> c5(MARK(and(s(and(and(tt, y0), y1)), z2))) A__LENGTH(cons(z0, and(s(and(and(s(y0), y1), y2)), z2))) -> c5(MARK(and(s(and(and(s(y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(and(and(y0, y1), y2)), z2))) -> c5(MARK(and(s(and(and(y0, y1), y2)), z2))) A__LENGTH(cons(z0, and(s(and(length(zeros), y0)), z2))) -> c5(MARK(and(s(and(length(zeros), y0)), z2))) A__LENGTH(cons(z0, and(s(and(length(and(y0, y1)), y2)), z2))) -> c5(MARK(and(s(and(length(and(y0, y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(and(length(length(y0)), y1)), z2))) -> c5(MARK(and(s(and(length(length(y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(and(length(cons(y0, y1)), y2)), z2))) -> c5(MARK(and(s(and(length(cons(y0, y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(and(length(s(y0)), y1)), z2))) -> c5(MARK(and(s(and(length(s(y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(and(length(y0), y1)), z2))) -> c5(MARK(and(s(and(length(y0), y1)), z2))) A__LENGTH(cons(z0, and(s(and(and(zeros, y0), y1)), z2))) -> c5(MARK(and(s(and(and(zeros, y0), y1)), z2))) A__LENGTH(cons(z0, and(s(length(and(and(y0, y1), y2))), z2))) -> c5(MARK(and(s(length(and(and(y0, y1), y2))), z2))) A__LENGTH(cons(z0, and(s(length(and(length(y0), y1))), z2))) -> c5(MARK(and(s(length(and(length(y0), y1))), z2))) A__LENGTH(cons(z0, and(s(length(and(cons(y0, y1), y2))), z2))) -> c5(MARK(and(s(length(and(cons(y0, y1), y2))), z2))) A__LENGTH(cons(z0, and(s(length(and(tt, y0))), z2))) -> c5(MARK(and(s(length(and(tt, y0))), z2))) A__LENGTH(cons(z0, and(s(length(and(s(y0), y1))), z2))) -> c5(MARK(and(s(length(and(s(y0), y1))), z2))) A__LENGTH(cons(z0, and(s(length(and(y0, y1))), z2))) -> c5(MARK(and(s(length(and(y0, y1))), z2))) A__LENGTH(cons(z0, and(s(length(and(zeros, y0))), z2))) -> c5(MARK(and(s(length(and(zeros, y0))), z2))) A__LENGTH(cons(z0, and(s(length(length(zeros))), z2))) -> c5(MARK(and(s(length(length(zeros))), z2))) A__LENGTH(cons(z0, and(s(length(length(and(y0, y1)))), z2))) -> c5(MARK(and(s(length(length(and(y0, y1)))), z2))) A__LENGTH(cons(z0, and(s(length(length(length(y0)))), z2))) -> c5(MARK(and(s(length(length(length(y0)))), z2))) A__LENGTH(cons(z0, and(s(length(length(cons(y0, y1)))), z2))) -> c5(MARK(and(s(length(length(cons(y0, y1)))), z2))) A__LENGTH(cons(z0, and(s(length(length(s(y0)))), z2))) -> c5(MARK(and(s(length(length(s(y0)))), z2))) A__LENGTH(cons(z0, and(s(length(length(y0))), z2))) -> c5(MARK(and(s(length(length(y0))), z2))) A__LENGTH(cons(z0, and(s(length(zeros)), z2))) -> c5(MARK(and(s(length(zeros)), z2))) A__LENGTH(cons(z0, and(s(cons(cons(y0, y1), y2)), z2))) -> c5(MARK(and(s(cons(cons(y0, y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(s(y0), y1)), z2))) -> c5(MARK(and(s(cons(s(y0), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(and(cons(y0, y1), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(cons(y0, y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(tt, y0), y1)), z2))) -> c5(MARK(and(s(cons(and(tt, y0), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(and(s(y0), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(s(y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(cons(y0, y1)), y2)), z2))) -> c5(MARK(and(s(cons(length(cons(y0, y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(s(y0)), y1)), z2))) -> c5(MARK(and(s(cons(length(s(y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(and(y0, y1), y2), y3), y4)), z2))) -> c5(MARK(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(length(y0), y1), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(and(length(y0), y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), z2))) -> c5(MARK(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(tt, y0), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(and(tt, y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(s(y0), y1), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(and(s(y0), y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(y0, y1), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(and(y0, y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(zeros), y0), y1)), z2))) -> c5(MARK(and(s(cons(and(length(zeros), y0), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(and(y0, y1)), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(length(and(y0, y1)), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(length(y0)), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(length(length(y0)), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(cons(y0, y1)), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(length(cons(y0, y1)), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(s(y0)), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(length(s(y0)), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(y0), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(length(y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(zeros, y0), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(and(zeros, y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(and(y0, y1), y2)), y3)), z2))) -> c5(MARK(and(s(cons(length(and(and(y0, y1), y2)), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(length(y0), y1)), y2)), z2))) -> c5(MARK(and(s(cons(length(and(length(y0), y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(cons(y0, y1), y2)), y3)), z2))) -> c5(MARK(and(s(cons(length(and(cons(y0, y1), y2)), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(tt, y0)), y1)), z2))) -> c5(MARK(and(s(cons(length(and(tt, y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(s(y0), y1)), y2)), z2))) -> c5(MARK(and(s(cons(length(and(s(y0), y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(y0, y1)), y2)), z2))) -> c5(MARK(and(s(cons(length(and(y0, y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(zeros, y0)), y1)), z2))) -> c5(MARK(and(s(cons(length(and(zeros, y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(zeros)), y0)), z2))) -> c5(MARK(and(s(cons(length(length(zeros)), y0)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(and(y0, y1))), y2)), z2))) -> c5(MARK(and(s(cons(length(length(and(y0, y1))), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(length(y0))), y1)), z2))) -> c5(MARK(and(s(cons(length(length(length(y0))), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(cons(y0, y1))), y2)), z2))) -> c5(MARK(and(s(cons(length(length(cons(y0, y1))), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(s(y0))), y1)), z2))) -> c5(MARK(and(s(cons(length(length(s(y0))), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(y0)), y1)), z2))) -> c5(MARK(and(s(cons(length(length(y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(zeros), y0)), z2))) -> c5(MARK(and(s(cons(length(zeros), y0)), z2))) ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) MARK(cons(and(and(cons(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(cons(y0, y1), y2), y3))) MARK(cons(and(and(tt, y0), y1), z1)) -> c10(MARK(and(and(tt, y0), y1))) MARK(cons(and(and(s(y0), y1), y2), z1)) -> c10(MARK(and(and(s(y0), y1), y2))) MARK(cons(and(and(y0, y1), y2), z1)) -> c10(MARK(and(and(y0, y1), y2))) MARK(cons(and(length(zeros), y0), z1)) -> c10(MARK(and(length(zeros), y0))) MARK(cons(and(length(and(y0, y1)), y2), z1)) -> c10(MARK(and(length(and(y0, y1)), y2))) MARK(cons(and(length(length(y0)), y1), z1)) -> c10(MARK(and(length(length(y0)), y1))) MARK(cons(and(length(cons(y0, y1)), y2), z1)) -> c10(MARK(and(length(cons(y0, y1)), y2))) MARK(cons(and(length(s(y0)), y1), z1)) -> c10(MARK(and(length(s(y0)), y1))) MARK(cons(and(length(y0), y1), z1)) -> c10(MARK(and(length(y0), y1))) MARK(cons(and(and(zeros, y0), y1), z1)) -> c10(MARK(and(and(zeros, y0), y1))) MARK(cons(length(and(and(y0, y1), y2)), z1)) -> c10(MARK(length(and(and(y0, y1), y2)))) MARK(cons(length(and(length(y0), y1)), z1)) -> c10(MARK(length(and(length(y0), y1)))) MARK(cons(length(and(cons(y0, y1), y2)), z1)) -> c10(MARK(length(and(cons(y0, y1), y2)))) MARK(cons(length(and(tt, y0)), z1)) -> c10(MARK(length(and(tt, y0)))) MARK(cons(length(and(s(y0), y1)), z1)) -> c10(MARK(length(and(s(y0), y1)))) MARK(cons(length(and(y0, y1)), z1)) -> c10(MARK(length(and(y0, y1)))) MARK(cons(length(and(zeros, y0)), z1)) -> c10(MARK(length(and(zeros, y0)))) MARK(cons(length(length(zeros)), z1)) -> c10(MARK(length(length(zeros)))) MARK(cons(length(length(and(y0, y1))), z1)) -> c10(MARK(length(length(and(y0, y1))))) MARK(cons(length(length(length(y0))), z1)) -> c10(MARK(length(length(length(y0))))) MARK(cons(length(length(cons(y0, y1))), z1)) -> c10(MARK(length(length(cons(y0, y1))))) MARK(cons(length(length(s(y0))), z1)) -> c10(MARK(length(length(s(y0))))) MARK(cons(length(length(y0)), z1)) -> c10(MARK(length(length(y0)))) MARK(cons(length(zeros), z1)) -> c10(MARK(length(zeros))) MARK(s(s(y0))) -> c14(MARK(s(y0))) MARK(s(and(cons(y0, y1), y2))) -> c14(MARK(and(cons(y0, y1), y2))) MARK(s(and(tt, y0))) -> c14(MARK(and(tt, y0))) MARK(s(and(s(y0), y1))) -> c14(MARK(and(s(y0), y1))) MARK(s(length(cons(y0, y1)))) -> c14(MARK(length(cons(y0, y1)))) MARK(s(length(s(y0)))) -> c14(MARK(length(s(y0)))) MARK(s(and(and(and(y0, y1), y2), y3))) -> c14(MARK(and(and(and(y0, y1), y2), y3))) MARK(s(and(and(length(y0), y1), y2))) -> c14(MARK(and(and(length(y0), y1), y2))) MARK(s(and(and(cons(y0, y1), y2), y3))) -> c14(MARK(and(and(cons(y0, y1), y2), y3))) MARK(s(and(and(tt, y0), y1))) -> c14(MARK(and(and(tt, y0), y1))) MARK(s(and(and(s(y0), y1), y2))) -> c14(MARK(and(and(s(y0), y1), y2))) MARK(s(and(and(y0, y1), y2))) -> c14(MARK(and(and(y0, y1), y2))) MARK(s(and(length(zeros), y0))) -> c14(MARK(and(length(zeros), y0))) MARK(s(and(length(and(y0, y1)), y2))) -> c14(MARK(and(length(and(y0, y1)), y2))) MARK(s(and(length(length(y0)), y1))) -> c14(MARK(and(length(length(y0)), y1))) MARK(s(and(length(cons(y0, y1)), y2))) -> c14(MARK(and(length(cons(y0, y1)), y2))) MARK(s(and(length(s(y0)), y1))) -> c14(MARK(and(length(s(y0)), y1))) MARK(s(and(length(y0), y1))) -> c14(MARK(and(length(y0), y1))) MARK(s(and(and(zeros, y0), y1))) -> c14(MARK(and(and(zeros, y0), y1))) MARK(s(length(and(and(y0, y1), y2)))) -> c14(MARK(length(and(and(y0, y1), y2)))) MARK(s(length(and(length(y0), y1)))) -> c14(MARK(length(and(length(y0), y1)))) MARK(s(length(and(cons(y0, y1), y2)))) -> c14(MARK(length(and(cons(y0, y1), y2)))) MARK(s(length(and(tt, y0)))) -> c14(MARK(length(and(tt, y0)))) MARK(s(length(and(s(y0), y1)))) -> c14(MARK(length(and(s(y0), y1)))) MARK(s(length(and(y0, y1)))) -> c14(MARK(length(and(y0, y1)))) MARK(s(length(and(zeros, y0)))) -> c14(MARK(length(and(zeros, y0)))) MARK(s(length(length(zeros)))) -> c14(MARK(length(length(zeros)))) MARK(s(length(length(and(y0, y1))))) -> c14(MARK(length(length(and(y0, y1))))) MARK(s(length(length(length(y0))))) -> c14(MARK(length(length(length(y0))))) MARK(s(length(length(cons(y0, y1))))) -> c14(MARK(length(length(cons(y0, y1))))) MARK(s(length(length(s(y0))))) -> c14(MARK(length(length(s(y0))))) MARK(s(length(length(y0)))) -> c14(MARK(length(length(y0)))) MARK(s(length(zeros))) -> c14(MARK(length(zeros))) MARK(s(cons(cons(y0, y1), y2))) -> c14(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c14(MARK(cons(s(y0), y1))) MARK(s(cons(and(cons(y0, y1), y2), y3))) -> c14(MARK(cons(and(cons(y0, y1), y2), y3))) MARK(s(cons(and(tt, y0), y1))) -> c14(MARK(cons(and(tt, y0), y1))) MARK(s(cons(and(s(y0), y1), y2))) -> c14(MARK(cons(and(s(y0), y1), y2))) MARK(s(cons(length(cons(y0, y1)), y2))) -> c14(MARK(cons(length(cons(y0, y1)), y2))) MARK(s(cons(length(s(y0)), y1))) -> 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MARK(and(s(cons(length(cons(y0, y1)), y2)), z1)) -> c8(MARK(s(cons(length(cons(y0, y1)), y2)))) MARK(and(s(cons(length(s(y0)), y1)), z1)) -> c8(MARK(s(cons(length(s(y0)), y1)))) MARK(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), z1)) -> c8(MARK(s(cons(and(and(and(y0, y1), y2), y3), y4)))) MARK(and(s(cons(and(and(length(y0), y1), y2), y3)), z1)) -> c8(MARK(s(cons(and(and(length(y0), y1), y2), y3)))) MARK(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), z1)) -> c8(MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) MARK(and(s(cons(and(and(tt, y0), y1), y2)), z1)) -> c8(MARK(s(cons(and(and(tt, y0), y1), y2)))) MARK(and(s(cons(and(and(s(y0), y1), y2), y3)), z1)) -> c8(MARK(s(cons(and(and(s(y0), y1), y2), y3)))) MARK(and(s(cons(and(and(y0, y1), y2), y3)), z1)) -> c8(MARK(s(cons(and(and(y0, y1), y2), y3)))) MARK(and(s(cons(and(length(zeros), y0), y1)), z1)) -> c8(MARK(s(cons(and(length(zeros), y0), y1)))) MARK(and(s(cons(and(length(and(y0, y1)), y2), y3)), z1)) -> c8(MARK(s(cons(and(length(and(y0, y1)), y2), y3)))) MARK(and(s(cons(and(length(length(y0)), y1), y2)), z1)) -> c8(MARK(s(cons(and(length(length(y0)), y1), y2)))) MARK(and(s(cons(and(length(cons(y0, y1)), y2), y3)), z1)) -> c8(MARK(s(cons(and(length(cons(y0, y1)), y2), y3)))) MARK(and(s(cons(and(length(s(y0)), y1), y2)), z1)) -> c8(MARK(s(cons(and(length(s(y0)), y1), y2)))) MARK(and(s(cons(and(length(y0), y1), y2)), z1)) -> c8(MARK(s(cons(and(length(y0), y1), y2)))) MARK(and(s(cons(and(and(zeros, y0), y1), y2)), z1)) -> c8(MARK(s(cons(and(and(zeros, y0), y1), y2)))) MARK(and(s(cons(length(and(and(y0, y1), y2)), y3)), z1)) -> c8(MARK(s(cons(length(and(and(y0, y1), y2)), y3)))) MARK(and(s(cons(length(and(length(y0), y1)), y2)), z1)) -> c8(MARK(s(cons(length(and(length(y0), y1)), y2)))) MARK(and(s(cons(length(and(cons(y0, y1), y2)), y3)), z1)) -> c8(MARK(s(cons(length(and(cons(y0, y1), y2)), y3)))) MARK(and(s(cons(length(and(tt, y0)), y1)), z1)) -> c8(MARK(s(cons(length(and(tt, y0)), y1)))) MARK(and(s(cons(length(and(s(y0), y1)), y2)), z1)) -> c8(MARK(s(cons(length(and(s(y0), y1)), y2)))) MARK(and(s(cons(length(and(y0, y1)), y2)), z1)) -> c8(MARK(s(cons(length(and(y0, y1)), y2)))) MARK(and(s(cons(length(and(zeros, y0)), y1)), z1)) -> c8(MARK(s(cons(length(and(zeros, y0)), y1)))) MARK(and(s(cons(length(length(zeros)), y0)), z1)) -> c8(MARK(s(cons(length(length(zeros)), y0)))) MARK(and(s(cons(length(length(and(y0, y1))), y2)), z1)) -> c8(MARK(s(cons(length(length(and(y0, y1))), y2)))) MARK(and(s(cons(length(length(length(y0))), y1)), z1)) -> c8(MARK(s(cons(length(length(length(y0))), y1)))) MARK(and(s(cons(length(length(cons(y0, y1))), y2)), z1)) -> c8(MARK(s(cons(length(length(cons(y0, y1))), y2)))) MARK(and(s(cons(length(length(s(y0))), y1)), z1)) -> c8(MARK(s(cons(length(length(s(y0))), y1)))) MARK(and(s(cons(length(length(y0)), y1)), z1)) -> c8(MARK(s(cons(length(length(y0)), y1)))) MARK(and(s(cons(length(zeros), y0)), z1)) -> c8(MARK(s(cons(length(zeros), y0)))) MARK(length(s(s(y0)))) -> c9(MARK(s(s(y0)))) MARK(length(s(and(cons(y0, y1), y2)))) -> c9(MARK(s(and(cons(y0, y1), y2)))) MARK(length(s(and(tt, y0)))) -> c9(MARK(s(and(tt, y0)))) MARK(length(s(and(s(y0), y1)))) -> c9(MARK(s(and(s(y0), y1)))) MARK(length(s(length(cons(y0, y1))))) -> c9(MARK(s(length(cons(y0, y1))))) MARK(length(s(length(s(y0))))) -> c9(MARK(s(length(s(y0))))) MARK(length(s(and(and(and(y0, y1), y2), y3)))) -> c9(MARK(s(and(and(and(y0, y1), y2), y3)))) MARK(length(s(and(and(length(y0), y1), y2)))) -> c9(MARK(s(and(and(length(y0), y1), y2)))) MARK(length(s(and(and(cons(y0, y1), y2), y3)))) -> c9(MARK(s(and(and(cons(y0, y1), y2), y3)))) MARK(length(s(and(and(tt, y0), y1)))) -> c9(MARK(s(and(and(tt, y0), y1)))) MARK(length(s(and(and(s(y0), y1), y2)))) -> c9(MARK(s(and(and(s(y0), y1), y2)))) MARK(length(s(and(and(y0, y1), y2)))) -> c9(MARK(s(and(and(y0, y1), y2)))) MARK(length(s(and(length(zeros), y0)))) -> c9(MARK(s(and(length(zeros), y0)))) MARK(length(s(and(length(and(y0, y1)), y2)))) -> c9(MARK(s(and(length(and(y0, y1)), y2)))) MARK(length(s(and(length(length(y0)), y1)))) -> c9(MARK(s(and(length(length(y0)), y1)))) MARK(length(s(and(length(cons(y0, y1)), y2)))) -> c9(MARK(s(and(length(cons(y0, y1)), y2)))) MARK(length(s(and(length(s(y0)), y1)))) -> c9(MARK(s(and(length(s(y0)), y1)))) MARK(length(s(and(length(y0), y1)))) -> c9(MARK(s(and(length(y0), y1)))) MARK(length(s(and(and(zeros, y0), y1)))) -> c9(MARK(s(and(and(zeros, y0), y1)))) MARK(length(s(length(and(and(y0, y1), y2))))) -> c9(MARK(s(length(and(and(y0, y1), y2))))) MARK(length(s(length(and(length(y0), y1))))) -> c9(MARK(s(length(and(length(y0), y1))))) MARK(length(s(length(and(cons(y0, y1), y2))))) -> c9(MARK(s(length(and(cons(y0, y1), y2))))) MARK(length(s(length(and(tt, y0))))) -> c9(MARK(s(length(and(tt, y0))))) MARK(length(s(length(and(s(y0), y1))))) -> c9(MARK(s(length(and(s(y0), y1))))) MARK(length(s(length(and(y0, y1))))) -> c9(MARK(s(length(and(y0, y1))))) MARK(length(s(length(and(zeros, y0))))) -> c9(MARK(s(length(and(zeros, y0))))) MARK(length(s(length(length(zeros))))) -> c9(MARK(s(length(length(zeros))))) MARK(length(s(length(length(and(y0, y1)))))) -> c9(MARK(s(length(length(and(y0, y1)))))) MARK(length(s(length(length(length(y0)))))) -> c9(MARK(s(length(length(length(y0)))))) MARK(length(s(length(length(cons(y0, y1)))))) -> c9(MARK(s(length(length(cons(y0, y1)))))) MARK(length(s(length(length(s(y0)))))) -> c9(MARK(s(length(length(s(y0)))))) MARK(length(s(length(length(y0))))) -> c9(MARK(s(length(length(y0))))) MARK(length(s(length(zeros)))) -> c9(MARK(s(length(zeros)))) MARK(length(s(cons(cons(y0, y1), y2)))) -> c9(MARK(s(cons(cons(y0, y1), y2)))) MARK(length(s(cons(s(y0), y1)))) -> c9(MARK(s(cons(s(y0), y1)))) MARK(length(s(cons(and(cons(y0, y1), y2), y3)))) -> c9(MARK(s(cons(and(cons(y0, y1), y2), y3)))) MARK(length(s(cons(and(tt, y0), y1)))) -> c9(MARK(s(cons(and(tt, y0), y1)))) MARK(length(s(cons(and(s(y0), y1), y2)))) -> c9(MARK(s(cons(and(s(y0), y1), y2)))) MARK(length(s(cons(length(cons(y0, y1)), y2)))) -> c9(MARK(s(cons(length(cons(y0, y1)), y2)))) MARK(length(s(cons(length(s(y0)), y1)))) -> c9(MARK(s(cons(length(s(y0)), y1)))) MARK(length(s(cons(and(and(and(y0, y1), y2), y3), y4)))) -> c9(MARK(s(cons(and(and(and(y0, y1), y2), y3), y4)))) MARK(length(s(cons(and(and(length(y0), y1), y2), y3)))) -> c9(MARK(s(cons(and(and(length(y0), y1), y2), y3)))) MARK(length(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) -> c9(MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) MARK(length(s(cons(and(and(tt, y0), y1), y2)))) -> c9(MARK(s(cons(and(and(tt, y0), y1), y2)))) MARK(length(s(cons(and(and(s(y0), y1), y2), y3)))) -> c9(MARK(s(cons(and(and(s(y0), y1), y2), y3)))) MARK(length(s(cons(and(and(y0, y1), y2), y3)))) -> c9(MARK(s(cons(and(and(y0, y1), y2), y3)))) MARK(length(s(cons(and(length(zeros), y0), y1)))) -> c9(MARK(s(cons(and(length(zeros), y0), y1)))) MARK(length(s(cons(and(length(and(y0, y1)), y2), y3)))) -> c9(MARK(s(cons(and(length(and(y0, y1)), y2), y3)))) MARK(length(s(cons(and(length(length(y0)), y1), y2)))) -> c9(MARK(s(cons(and(length(length(y0)), y1), y2)))) MARK(length(s(cons(and(length(cons(y0, y1)), y2), y3)))) -> c9(MARK(s(cons(and(length(cons(y0, y1)), y2), y3)))) MARK(length(s(cons(and(length(s(y0)), y1), y2)))) -> c9(MARK(s(cons(and(length(s(y0)), y1), y2)))) MARK(length(s(cons(and(length(y0), y1), y2)))) -> c9(MARK(s(cons(and(length(y0), y1), y2)))) MARK(length(s(cons(and(and(zeros, y0), y1), y2)))) -> c9(MARK(s(cons(and(and(zeros, y0), y1), y2)))) MARK(length(s(cons(length(and(and(y0, y1), y2)), y3)))) -> c9(MARK(s(cons(length(and(and(y0, y1), y2)), y3)))) MARK(length(s(cons(length(and(length(y0), y1)), y2)))) -> c9(MARK(s(cons(length(and(length(y0), y1)), y2)))) MARK(length(s(cons(length(and(cons(y0, y1), y2)), y3)))) -> c9(MARK(s(cons(length(and(cons(y0, y1), y2)), y3)))) MARK(length(s(cons(length(and(tt, y0)), y1)))) -> c9(MARK(s(cons(length(and(tt, y0)), y1)))) 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z2))) A__LENGTH(cons(z0, and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), z2))) -> c5(MARK(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(tt, y0), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(and(tt, y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(s(y0), y1), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(and(s(y0), y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(y0, y1), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(and(y0, y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(zeros), y0), y1)), z2))) -> c5(MARK(and(s(cons(and(length(zeros), y0), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(and(y0, y1)), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(length(and(y0, y1)), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(length(y0)), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(length(length(y0)), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(cons(y0, y1)), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(length(cons(y0, y1)), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(s(y0)), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(length(s(y0)), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(y0), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(length(y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(zeros, y0), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(and(zeros, y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(and(y0, y1), y2)), y3)), z2))) -> c5(MARK(and(s(cons(length(and(and(y0, y1), y2)), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(length(y0), y1)), y2)), z2))) -> c5(MARK(and(s(cons(length(and(length(y0), y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(cons(y0, y1), y2)), y3)), z2))) -> c5(MARK(and(s(cons(length(and(cons(y0, y1), y2)), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(tt, y0)), y1)), z2))) -> c5(MARK(and(s(cons(length(and(tt, y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(s(y0), y1)), y2)), z2))) -> c5(MARK(and(s(cons(length(and(s(y0), y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(y0, y1)), y2)), z2))) -> c5(MARK(and(s(cons(length(and(y0, y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(zeros, y0)), y1)), z2))) -> c5(MARK(and(s(cons(length(and(zeros, y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(zeros)), y0)), z2))) -> c5(MARK(and(s(cons(length(length(zeros)), y0)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(and(y0, y1))), y2)), z2))) -> c5(MARK(and(s(cons(length(length(and(y0, y1))), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(length(y0))), y1)), z2))) -> c5(MARK(and(s(cons(length(length(length(y0))), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(cons(y0, y1))), y2)), z2))) -> c5(MARK(and(s(cons(length(length(cons(y0, y1))), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(s(y0))), y1)), z2))) -> c5(MARK(and(s(cons(length(length(s(y0))), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(y0)), y1)), z2))) -> c5(MARK(and(s(cons(length(length(y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(zeros), y0)), z2))) -> c5(MARK(and(s(cons(length(zeros), y0)), z2))) S tuples: A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) MARK(cons(and(and(cons(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(cons(y0, y1), y2), y3))) MARK(cons(and(and(tt, y0), y1), z1)) -> c10(MARK(and(and(tt, y0), y1))) MARK(cons(and(and(s(y0), y1), y2), z1)) -> c10(MARK(and(and(s(y0), y1), y2))) MARK(cons(and(and(y0, y1), y2), z1)) -> c10(MARK(and(and(y0, y1), y2))) MARK(cons(and(length(zeros), y0), z1)) -> c10(MARK(and(length(zeros), y0))) MARK(cons(and(length(and(y0, y1)), y2), z1)) -> c10(MARK(and(length(and(y0, y1)), y2))) MARK(cons(and(length(length(y0)), y1), z1)) -> c10(MARK(and(length(length(y0)), y1))) MARK(cons(and(length(cons(y0, y1)), y2), z1)) -> c10(MARK(and(length(cons(y0, y1)), y2))) MARK(cons(and(length(s(y0)), y1), z1)) -> c10(MARK(and(length(s(y0)), y1))) MARK(cons(and(length(y0), y1), z1)) -> c10(MARK(and(length(y0), y1))) MARK(cons(and(and(zeros, y0), y1), z1)) -> c10(MARK(and(and(zeros, y0), y1))) MARK(cons(length(and(and(y0, y1), y2)), z1)) -> c10(MARK(length(and(and(y0, y1), y2)))) MARK(cons(length(and(length(y0), y1)), z1)) -> c10(MARK(length(and(length(y0), y1)))) MARK(cons(length(and(cons(y0, y1), y2)), z1)) -> c10(MARK(length(and(cons(y0, y1), y2)))) MARK(cons(length(and(tt, y0)), z1)) -> c10(MARK(length(and(tt, y0)))) MARK(cons(length(and(s(y0), y1)), z1)) -> c10(MARK(length(and(s(y0), y1)))) MARK(cons(length(and(y0, y1)), z1)) -> c10(MARK(length(and(y0, y1)))) MARK(cons(length(and(zeros, y0)), z1)) -> c10(MARK(length(and(zeros, y0)))) MARK(cons(length(length(zeros)), z1)) -> c10(MARK(length(length(zeros)))) MARK(cons(length(length(and(y0, y1))), z1)) -> c10(MARK(length(length(and(y0, y1))))) MARK(cons(length(length(length(y0))), z1)) -> c10(MARK(length(length(length(y0))))) MARK(cons(length(length(cons(y0, y1))), z1)) -> c10(MARK(length(length(cons(y0, y1))))) MARK(cons(length(length(s(y0))), z1)) -> c10(MARK(length(length(s(y0))))) MARK(cons(length(length(y0)), z1)) -> c10(MARK(length(length(y0)))) MARK(cons(length(zeros), z1)) -> c10(MARK(length(zeros))) MARK(s(s(y0))) -> c14(MARK(s(y0))) MARK(s(and(cons(y0, y1), y2))) -> c14(MARK(and(cons(y0, y1), y2))) MARK(s(and(tt, y0))) -> c14(MARK(and(tt, y0))) MARK(s(and(s(y0), y1))) -> c14(MARK(and(s(y0), y1))) MARK(s(length(cons(y0, y1)))) -> c14(MARK(length(cons(y0, y1)))) MARK(s(length(s(y0)))) -> c14(MARK(length(s(y0)))) MARK(s(and(and(and(y0, y1), y2), y3))) -> c14(MARK(and(and(and(y0, y1), y2), y3))) MARK(s(and(and(length(y0), y1), y2))) -> c14(MARK(and(and(length(y0), y1), y2))) MARK(s(and(and(cons(y0, y1), y2), y3))) -> c14(MARK(and(and(cons(y0, y1), y2), y3))) MARK(s(and(and(tt, y0), y1))) -> c14(MARK(and(and(tt, y0), y1))) MARK(s(and(and(s(y0), y1), y2))) -> c14(MARK(and(and(s(y0), y1), y2))) MARK(s(and(and(y0, y1), y2))) -> c14(MARK(and(and(y0, y1), y2))) MARK(s(and(length(zeros), y0))) -> c14(MARK(and(length(zeros), y0))) MARK(s(and(length(and(y0, y1)), y2))) -> c14(MARK(and(length(and(y0, y1)), y2))) MARK(s(and(length(length(y0)), y1))) -> c14(MARK(and(length(length(y0)), y1))) MARK(s(and(length(cons(y0, y1)), y2))) -> c14(MARK(and(length(cons(y0, y1)), y2))) MARK(s(and(length(s(y0)), y1))) -> c14(MARK(and(length(s(y0)), y1))) MARK(s(and(length(y0), y1))) -> c14(MARK(and(length(y0), y1))) MARK(s(and(and(zeros, y0), y1))) -> c14(MARK(and(and(zeros, y0), y1))) MARK(s(length(and(and(y0, y1), y2)))) -> c14(MARK(length(and(and(y0, y1), y2)))) MARK(s(length(and(length(y0), y1)))) -> c14(MARK(length(and(length(y0), y1)))) MARK(s(length(and(cons(y0, y1), y2)))) -> c14(MARK(length(and(cons(y0, y1), y2)))) MARK(s(length(and(tt, y0)))) -> c14(MARK(length(and(tt, y0)))) MARK(s(length(and(s(y0), y1)))) -> c14(MARK(length(and(s(y0), y1)))) MARK(s(length(and(y0, y1)))) -> c14(MARK(length(and(y0, y1)))) MARK(s(length(and(zeros, y0)))) -> c14(MARK(length(and(zeros, y0)))) MARK(s(length(length(zeros)))) -> c14(MARK(length(length(zeros)))) MARK(s(length(length(and(y0, y1))))) -> c14(MARK(length(length(and(y0, y1))))) MARK(s(length(length(length(y0))))) -> c14(MARK(length(length(length(y0))))) MARK(s(length(length(cons(y0, y1))))) -> c14(MARK(length(length(cons(y0, y1))))) MARK(s(length(length(s(y0))))) -> c14(MARK(length(length(s(y0))))) MARK(s(length(length(y0)))) -> c14(MARK(length(length(y0)))) MARK(s(length(zeros))) -> c14(MARK(length(zeros))) MARK(s(cons(cons(y0, y1), y2))) -> c14(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c14(MARK(cons(s(y0), y1))) MARK(s(cons(and(cons(y0, y1), y2), y3))) -> c14(MARK(cons(and(cons(y0, y1), y2), y3))) MARK(s(cons(and(tt, y0), y1))) -> c14(MARK(cons(and(tt, y0), y1))) MARK(s(cons(and(s(y0), y1), y2))) -> c14(MARK(cons(and(s(y0), y1), y2))) MARK(s(cons(length(cons(y0, y1)), y2))) -> c14(MARK(cons(length(cons(y0, y1)), y2))) MARK(s(cons(length(s(y0)), y1))) -> c14(MARK(cons(length(s(y0)), y1))) MARK(s(cons(and(and(and(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(and(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(length(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(length(y0), y1), y2), y3))) MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(cons(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(tt, y0), y1), y2))) -> c14(MARK(cons(and(and(tt, y0), y1), y2))) MARK(s(cons(and(and(s(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(s(y0), y1), y2), y3))) MARK(s(cons(and(and(y0, y1), y2), y3))) -> c14(MARK(cons(and(and(y0, y1), y2), y3))) MARK(s(cons(and(length(zeros), y0), y1))) -> c14(MARK(cons(and(length(zeros), y0), y1))) MARK(s(cons(and(length(and(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(and(y0, y1)), y2), y3))) MARK(s(cons(and(length(length(y0)), y1), y2))) -> c14(MARK(cons(and(length(length(y0)), y1), y2))) MARK(s(cons(and(length(cons(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(cons(y0, y1)), y2), y3))) MARK(s(cons(and(length(s(y0)), y1), y2))) -> c14(MARK(cons(and(length(s(y0)), y1), y2))) MARK(s(cons(and(length(y0), y1), y2))) -> c14(MARK(cons(and(length(y0), y1), y2))) MARK(s(cons(and(and(zeros, y0), y1), y2))) -> c14(MARK(cons(and(and(zeros, y0), y1), y2))) MARK(s(cons(length(and(and(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(and(y0, y1), y2)), y3))) MARK(s(cons(length(and(length(y0), y1)), y2))) -> c14(MARK(cons(length(and(length(y0), y1)), y2))) MARK(s(cons(length(and(cons(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(cons(y0, y1), y2)), y3))) MARK(s(cons(length(and(tt, y0)), y1))) -> c14(MARK(cons(length(and(tt, y0)), y1))) MARK(s(cons(length(and(s(y0), y1)), y2))) -> c14(MARK(cons(length(and(s(y0), y1)), y2))) MARK(s(cons(length(and(y0, y1)), y2))) -> c14(MARK(cons(length(and(y0, y1)), y2))) MARK(s(cons(length(and(zeros, y0)), y1))) -> c14(MARK(cons(length(and(zeros, y0)), y1))) MARK(s(cons(length(length(zeros)), y0))) -> c14(MARK(cons(length(length(zeros)), y0))) MARK(s(cons(length(length(and(y0, y1))), y2))) -> c14(MARK(cons(length(length(and(y0, y1))), y2))) MARK(s(cons(length(length(length(y0))), y1))) -> c14(MARK(cons(length(length(length(y0))), y1))) MARK(s(cons(length(length(cons(y0, y1))), y2))) -> c14(MARK(cons(length(length(cons(y0, y1))), y2))) MARK(s(cons(length(length(s(y0))), y1))) -> c14(MARK(cons(length(length(s(y0))), y1))) MARK(s(cons(length(length(y0)), y1))) -> c14(MARK(cons(length(length(y0)), y1))) MARK(s(cons(length(zeros), y0))) -> c14(MARK(cons(length(zeros), y0))) A__LENGTH(cons(z0, s(s(y0)))) -> c5(MARK(s(s(y0)))) A__LENGTH(cons(z0, s(and(cons(y0, y1), y2)))) -> c5(MARK(s(and(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(tt, y0)))) -> c5(MARK(s(and(tt, y0)))) A__LENGTH(cons(z0, s(and(s(y0), y1)))) -> c5(MARK(s(and(s(y0), y1)))) A__LENGTH(cons(z0, s(length(cons(y0, y1))))) -> c5(MARK(s(length(cons(y0, y1))))) A__LENGTH(cons(z0, s(length(s(y0))))) -> c5(MARK(s(length(s(y0))))) A__LENGTH(cons(z0, s(and(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(length(y0), y1), y2)))) -> c5(MARK(s(and(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(tt, y0), y1)))) -> c5(MARK(s(and(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(and(and(s(y0), y1), y2)))) -> c5(MARK(s(and(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(y0, y1), y2)))) -> c5(MARK(s(and(and(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(length(zeros), y0)))) -> c5(MARK(s(and(length(zeros), y0)))) A__LENGTH(cons(z0, s(and(length(and(y0, y1)), y2)))) -> c5(MARK(s(and(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(length(y0)), y1)))) -> c5(MARK(s(and(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(cons(y0, y1)), y2)))) -> c5(MARK(s(and(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(s(y0)), y1)))) -> c5(MARK(s(and(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(y0), y1)))) -> c5(MARK(s(and(length(y0), y1)))) A__LENGTH(cons(z0, s(and(and(zeros, y0), y1)))) -> c5(MARK(s(and(and(zeros, y0), y1)))) A__LENGTH(cons(z0, s(length(and(and(y0, y1), y2))))) -> c5(MARK(s(length(and(and(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(length(y0), y1))))) -> c5(MARK(s(length(and(length(y0), y1))))) A__LENGTH(cons(z0, s(length(and(cons(y0, y1), y2))))) -> c5(MARK(s(length(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(tt, y0))))) -> c5(MARK(s(length(and(tt, y0))))) A__LENGTH(cons(z0, s(length(and(s(y0), y1))))) -> c5(MARK(s(length(and(s(y0), y1))))) A__LENGTH(cons(z0, s(length(and(y0, y1))))) -> c5(MARK(s(length(and(y0, y1))))) A__LENGTH(cons(z0, s(length(and(zeros, y0))))) -> c5(MARK(s(length(and(zeros, y0))))) A__LENGTH(cons(z0, s(length(length(zeros))))) -> c5(MARK(s(length(length(zeros))))) A__LENGTH(cons(z0, s(length(length(and(y0, y1)))))) -> c5(MARK(s(length(length(and(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(length(y0)))))) -> c5(MARK(s(length(length(length(y0)))))) A__LENGTH(cons(z0, s(length(length(cons(y0, y1)))))) -> c5(MARK(s(length(length(cons(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(s(y0)))))) -> c5(MARK(s(length(length(s(y0)))))) A__LENGTH(cons(z0, s(length(length(y0))))) -> c5(MARK(s(length(length(y0))))) A__LENGTH(cons(z0, s(length(zeros)))) -> c5(MARK(s(length(zeros)))) A__LENGTH(cons(z0, s(cons(cons(y0, y1), y2)))) -> c5(MARK(s(cons(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(cons(s(y0), y1)))) -> c5(MARK(s(cons(s(y0), y1)))) A__LENGTH(cons(z0, s(cons(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(tt, y0), y1)))) -> c5(MARK(s(cons(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(cons(and(s(y0), y1), y2)))) -> c5(MARK(s(cons(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(length(cons(y0, y1)), y2)))) -> c5(MARK(s(cons(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(s(y0)), y1)))) -> c5(MARK(s(cons(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(cons(and(and(and(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(and(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(length(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(length(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(cons(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(tt, y0), y1), y2)))) -> c5(MARK(s(cons(and(and(tt, y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(and(s(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(s(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(zeros), y0), y1)))) -> c5(MARK(s(cons(and(length(zeros), y0), y1)))) A__LENGTH(cons(z0, s(cons(and(length(and(y0, y1)), y2), y3)))) -> c5(MARK(s(cons(and(length(and(y0, y1)), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(length(y0)), y1), y2)))) -> c5(MARK(s(cons(and(length(length(y0)), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(length(cons(y0, y1)), y2), y3)))) -> c5(MARK(s(cons(and(length(cons(y0, y1)), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(s(y0)), y1), y2)))) -> c5(MARK(s(cons(and(length(s(y0)), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(length(y0), y1), y2)))) -> c5(MARK(s(cons(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(and(zeros, y0), y1), y2)))) -> c5(MARK(s(cons(and(and(zeros, y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(length(and(and(y0, y1), y2)), y3)))) -> c5(MARK(s(cons(length(and(and(y0, y1), y2)), y3)))) A__LENGTH(cons(z0, s(cons(length(and(length(y0), y1)), y2)))) -> c5(MARK(s(cons(length(and(length(y0), y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(cons(y0, y1), y2)), y3)))) -> c5(MARK(s(cons(length(and(cons(y0, y1), y2)), y3)))) A__LENGTH(cons(z0, s(cons(length(and(tt, y0)), y1)))) -> c5(MARK(s(cons(length(and(tt, y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(and(s(y0), y1)), y2)))) -> c5(MARK(s(cons(length(and(s(y0), y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(y0, y1)), y2)))) -> c5(MARK(s(cons(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(zeros, y0)), y1)))) -> c5(MARK(s(cons(length(and(zeros, y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(length(zeros)), y0)))) -> c5(MARK(s(cons(length(length(zeros)), y0)))) A__LENGTH(cons(z0, s(cons(length(length(and(y0, y1))), y2)))) -> c5(MARK(s(cons(length(length(and(y0, y1))), y2)))) A__LENGTH(cons(z0, s(cons(length(length(length(y0))), y1)))) -> c5(MARK(s(cons(length(length(length(y0))), y1)))) A__LENGTH(cons(z0, s(cons(length(length(cons(y0, y1))), y2)))) -> c5(MARK(s(cons(length(length(cons(y0, y1))), y2)))) A__LENGTH(cons(z0, s(cons(length(length(s(y0))), y1)))) -> c5(MARK(s(cons(length(length(s(y0))), y1)))) A__LENGTH(cons(z0, s(cons(length(length(y0)), y1)))) -> c5(MARK(s(cons(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(zeros), y0)))) -> c5(MARK(s(cons(length(zeros), y0)))) MARK(and(cons(cons(y0, y1), z1), z2)) -> c8(MARK(cons(cons(y0, y1), z1))) MARK(and(cons(s(y0), z1), z2)) -> c8(MARK(cons(s(y0), z1))) MARK(and(cons(and(cons(y0, y1), y2), z1), z2)) -> c8(MARK(cons(and(cons(y0, y1), y2), z1))) MARK(and(cons(and(tt, y0), z1), z2)) -> c8(MARK(cons(and(tt, y0), z1))) MARK(and(cons(and(s(y0), y1), z1), z2)) -> c8(MARK(cons(and(s(y0), y1), z1))) MARK(and(cons(length(cons(y0, y1)), z1), z2)) -> c8(MARK(cons(length(cons(y0, y1)), z1))) MARK(and(cons(length(s(y0)), z1), z2)) -> c8(MARK(cons(length(s(y0)), z1))) MARK(and(cons(and(and(and(y0, y1), y2), y3), z1), z2)) -> c8(MARK(cons(and(and(and(y0, y1), y2), y3), z1))) MARK(and(cons(and(and(length(y0), y1), y2), z1), z2)) -> c8(MARK(cons(and(and(length(y0), y1), y2), z1))) MARK(and(cons(and(and(cons(y0, y1), y2), y3), z1), z2)) -> c8(MARK(cons(and(and(cons(y0, y1), y2), y3), z1))) MARK(and(cons(and(and(tt, y0), y1), z1), z2)) -> c8(MARK(cons(and(and(tt, y0), y1), z1))) MARK(and(cons(and(and(s(y0), y1), y2), z1), z2)) -> c8(MARK(cons(and(and(s(y0), y1), y2), z1))) MARK(and(cons(and(and(y0, y1), y2), z1), z2)) -> c8(MARK(cons(and(and(y0, y1), y2), z1))) MARK(and(cons(and(length(zeros), y0), z1), z2)) -> c8(MARK(cons(and(length(zeros), y0), z1))) MARK(and(cons(and(length(and(y0, y1)), y2), z1), z2)) -> c8(MARK(cons(and(length(and(y0, y1)), y2), z1))) MARK(and(cons(and(length(length(y0)), y1), z1), z2)) -> c8(MARK(cons(and(length(length(y0)), y1), z1))) MARK(and(cons(and(length(cons(y0, y1)), y2), z1), z2)) -> c8(MARK(cons(and(length(cons(y0, y1)), y2), z1))) MARK(and(cons(and(length(s(y0)), y1), z1), z2)) -> c8(MARK(cons(and(length(s(y0)), y1), z1))) MARK(and(cons(and(length(y0), y1), z1), z2)) -> c8(MARK(cons(and(length(y0), y1), z1))) MARK(and(cons(and(and(zeros, y0), y1), z1), z2)) -> c8(MARK(cons(and(and(zeros, y0), y1), z1))) MARK(and(cons(length(and(and(y0, y1), y2)), z1), z2)) -> c8(MARK(cons(length(and(and(y0, y1), y2)), z1))) MARK(and(cons(length(and(length(y0), y1)), z1), z2)) -> c8(MARK(cons(length(and(length(y0), y1)), z1))) MARK(and(cons(length(and(cons(y0, y1), y2)), z1), z2)) -> c8(MARK(cons(length(and(cons(y0, y1), y2)), z1))) MARK(and(cons(length(and(tt, y0)), z1), z2)) -> c8(MARK(cons(length(and(tt, y0)), z1))) MARK(and(cons(length(and(s(y0), y1)), z1), z2)) -> c8(MARK(cons(length(and(s(y0), y1)), z1))) MARK(and(cons(length(and(y0, y1)), z1), z2)) -> c8(MARK(cons(length(and(y0, y1)), z1))) MARK(and(cons(length(and(zeros, y0)), z1), z2)) -> c8(MARK(cons(length(and(zeros, y0)), z1))) MARK(and(cons(length(length(zeros)), z1), z2)) -> c8(MARK(cons(length(length(zeros)), z1))) MARK(and(cons(length(length(and(y0, y1))), z1), z2)) -> c8(MARK(cons(length(length(and(y0, y1))), z1))) MARK(and(cons(length(length(length(y0))), z1), z2)) -> c8(MARK(cons(length(length(length(y0))), z1))) MARK(and(cons(length(length(cons(y0, y1))), z1), z2)) -> c8(MARK(cons(length(length(cons(y0, y1))), z1))) MARK(and(cons(length(length(s(y0))), z1), z2)) -> c8(MARK(cons(length(length(s(y0))), z1))) MARK(and(cons(length(length(y0)), z1), z2)) -> c8(MARK(cons(length(length(y0)), z1))) MARK(and(cons(length(zeros), z1), z2)) -> c8(MARK(cons(length(zeros), z1))) MARK(and(tt, cons(y0, y1))) -> c8(A__AND(tt, cons(y0, y1))) MARK(and(tt, s(y0))) -> c8(A__AND(tt, s(y0))) MARK(and(tt, and(cons(y0, y1), y2))) -> c8(A__AND(tt, and(cons(y0, y1), y2))) MARK(and(tt, and(tt, y0))) -> c8(A__AND(tt, and(tt, y0))) MARK(and(tt, and(s(y0), y1))) -> c8(A__AND(tt, and(s(y0), y1))) MARK(and(tt, length(cons(y0, y1)))) -> c8(A__AND(tt, length(cons(y0, y1)))) MARK(and(tt, length(s(y0)))) -> c8(A__AND(tt, length(s(y0)))) MARK(and(tt, and(and(and(y0, y1), y2), y3))) -> c8(A__AND(tt, and(and(and(y0, y1), y2), y3))) MARK(and(tt, and(and(length(y0), y1), y2))) -> c8(A__AND(tt, and(and(length(y0), y1), y2))) MARK(and(tt, and(and(cons(y0, y1), y2), y3))) -> c8(A__AND(tt, and(and(cons(y0, y1), y2), y3))) MARK(and(tt, and(and(tt, y0), y1))) -> c8(A__AND(tt, and(and(tt, y0), y1))) MARK(and(tt, and(and(s(y0), y1), y2))) -> c8(A__AND(tt, and(and(s(y0), y1), y2))) MARK(and(tt, and(and(y0, y1), y2))) -> 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A__LENGTH(cons(z0, and(cons(cons(y0, y1), y2), z2))) -> c5(MARK(and(cons(cons(y0, y1), y2), z2))) A__LENGTH(cons(z0, and(cons(s(y0), y1), z2))) -> c5(MARK(and(cons(s(y0), y1), z2))) A__LENGTH(cons(z0, and(cons(and(cons(y0, y1), y2), y3), z2))) -> c5(MARK(and(cons(and(cons(y0, y1), y2), y3), z2))) A__LENGTH(cons(z0, and(cons(and(tt, y0), y1), z2))) -> c5(MARK(and(cons(and(tt, y0), y1), z2))) A__LENGTH(cons(z0, and(cons(and(s(y0), y1), y2), z2))) -> c5(MARK(and(cons(and(s(y0), y1), y2), z2))) A__LENGTH(cons(z0, and(cons(length(cons(y0, y1)), y2), z2))) -> c5(MARK(and(cons(length(cons(y0, y1)), y2), z2))) A__LENGTH(cons(z0, and(cons(length(s(y0)), y1), z2))) -> c5(MARK(and(cons(length(s(y0)), y1), z2))) A__LENGTH(cons(z0, and(cons(and(and(and(y0, y1), y2), y3), y4), z2))) -> c5(MARK(and(cons(and(and(and(y0, y1), y2), y3), y4), z2))) A__LENGTH(cons(z0, and(cons(and(and(length(y0), y1), y2), y3), z2))) -> c5(MARK(and(cons(and(and(length(y0), y1), y2), y3), z2))) A__LENGTH(cons(z0, and(cons(and(and(cons(y0, y1), y2), y3), y4), z2))) -> c5(MARK(and(cons(and(and(cons(y0, y1), y2), y3), y4), z2))) A__LENGTH(cons(z0, and(cons(and(and(tt, y0), y1), y2), z2))) -> c5(MARK(and(cons(and(and(tt, y0), y1), y2), z2))) A__LENGTH(cons(z0, and(cons(and(and(s(y0), y1), y2), y3), z2))) -> c5(MARK(and(cons(and(and(s(y0), y1), y2), y3), z2))) A__LENGTH(cons(z0, and(cons(and(and(y0, y1), y2), y3), z2))) -> c5(MARK(and(cons(and(and(y0, y1), y2), y3), z2))) A__LENGTH(cons(z0, and(cons(and(length(zeros), y0), y1), z2))) -> c5(MARK(and(cons(and(length(zeros), y0), y1), z2))) A__LENGTH(cons(z0, and(cons(and(length(and(y0, y1)), y2), y3), z2))) -> c5(MARK(and(cons(and(length(and(y0, y1)), y2), y3), z2))) A__LENGTH(cons(z0, and(cons(and(length(length(y0)), y1), y2), z2))) -> c5(MARK(and(cons(and(length(length(y0)), y1), y2), z2))) A__LENGTH(cons(z0, and(cons(and(length(cons(y0, y1)), y2), y3), z2))) -> c5(MARK(and(cons(and(length(cons(y0, y1)), y2), y3), z2))) A__LENGTH(cons(z0, and(cons(and(length(s(y0)), y1), y2), z2))) -> c5(MARK(and(cons(and(length(s(y0)), y1), y2), z2))) A__LENGTH(cons(z0, and(cons(and(length(y0), y1), y2), z2))) -> c5(MARK(and(cons(and(length(y0), y1), y2), z2))) A__LENGTH(cons(z0, and(cons(and(and(zeros, y0), y1), y2), z2))) -> c5(MARK(and(cons(and(and(zeros, y0), y1), y2), z2))) A__LENGTH(cons(z0, and(cons(length(and(and(y0, y1), y2)), y3), z2))) -> c5(MARK(and(cons(length(and(and(y0, y1), y2)), y3), z2))) A__LENGTH(cons(z0, and(cons(length(and(length(y0), y1)), y2), z2))) -> c5(MARK(and(cons(length(and(length(y0), y1)), y2), z2))) A__LENGTH(cons(z0, and(cons(length(and(cons(y0, y1), y2)), y3), z2))) -> c5(MARK(and(cons(length(and(cons(y0, y1), y2)), y3), z2))) A__LENGTH(cons(z0, and(cons(length(and(tt, y0)), y1), z2))) -> c5(MARK(and(cons(length(and(tt, y0)), y1), z2))) A__LENGTH(cons(z0, and(cons(length(and(s(y0), y1)), y2), z2))) -> c5(MARK(and(cons(length(and(s(y0), y1)), y2), z2))) A__LENGTH(cons(z0, and(cons(length(and(y0, y1)), y2), z2))) -> c5(MARK(and(cons(length(and(y0, y1)), y2), z2))) A__LENGTH(cons(z0, and(cons(length(and(zeros, y0)), y1), z2))) -> c5(MARK(and(cons(length(and(zeros, y0)), y1), z2))) A__LENGTH(cons(z0, and(cons(length(length(zeros)), y0), z2))) -> c5(MARK(and(cons(length(length(zeros)), y0), z2))) A__LENGTH(cons(z0, and(cons(length(length(and(y0, y1))), y2), z2))) -> c5(MARK(and(cons(length(length(and(y0, y1))), y2), z2))) A__LENGTH(cons(z0, and(cons(length(length(length(y0))), y1), z2))) -> c5(MARK(and(cons(length(length(length(y0))), y1), z2))) A__LENGTH(cons(z0, and(cons(length(length(cons(y0, y1))), y2), z2))) -> c5(MARK(and(cons(length(length(cons(y0, y1))), y2), z2))) A__LENGTH(cons(z0, and(cons(length(length(s(y0))), y1), z2))) -> c5(MARK(and(cons(length(length(s(y0))), y1), z2))) A__LENGTH(cons(z0, and(cons(length(length(y0)), y1), z2))) -> c5(MARK(and(cons(length(length(y0)), y1), z2))) A__LENGTH(cons(z0, and(cons(length(zeros), y0), z2))) -> c5(MARK(and(cons(length(zeros), y0), z2))) A__LENGTH(cons(z0, and(tt, cons(y0, y1)))) -> c5(MARK(and(tt, cons(y0, y1)))) A__LENGTH(cons(z0, and(tt, s(y0)))) -> c5(MARK(and(tt, s(y0)))) A__LENGTH(cons(z0, and(tt, and(cons(y0, y1), y2)))) -> c5(MARK(and(tt, and(cons(y0, y1), y2)))) A__LENGTH(cons(z0, and(tt, and(tt, y0)))) -> c5(MARK(and(tt, and(tt, y0)))) A__LENGTH(cons(z0, and(tt, and(s(y0), y1)))) -> c5(MARK(and(tt, and(s(y0), y1)))) A__LENGTH(cons(z0, and(tt, length(cons(y0, y1))))) -> c5(MARK(and(tt, length(cons(y0, y1))))) A__LENGTH(cons(z0, and(tt, length(s(y0))))) -> c5(MARK(and(tt, length(s(y0))))) A__LENGTH(cons(z0, and(tt, and(and(and(y0, y1), y2), y3)))) -> c5(MARK(and(tt, and(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, and(tt, and(and(length(y0), y1), y2)))) -> c5(MARK(and(tt, and(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, and(tt, and(and(cons(y0, y1), y2), y3)))) -> c5(MARK(and(tt, and(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, and(tt, and(and(tt, y0), y1)))) -> c5(MARK(and(tt, and(and(tt, y0), y1)))) A__LENGTH(cons(z0, and(tt, and(and(s(y0), y1), y2)))) -> c5(MARK(and(tt, and(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, and(tt, and(and(y0, y1), y2)))) -> c5(MARK(and(tt, and(and(y0, y1), y2)))) A__LENGTH(cons(z0, and(tt, and(length(zeros), y0)))) -> c5(MARK(and(tt, and(length(zeros), y0)))) A__LENGTH(cons(z0, and(tt, and(length(and(y0, y1)), y2)))) -> c5(MARK(and(tt, and(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, and(tt, and(length(length(y0)), y1)))) -> c5(MARK(and(tt, and(length(length(y0)), y1)))) A__LENGTH(cons(z0, and(tt, and(length(cons(y0, y1)), y2)))) -> c5(MARK(and(tt, and(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, and(tt, and(length(s(y0)), y1)))) -> c5(MARK(and(tt, and(length(s(y0)), y1)))) A__LENGTH(cons(z0, and(tt, and(length(y0), y1)))) -> c5(MARK(and(tt, and(length(y0), y1)))) A__LENGTH(cons(z0, and(tt, and(and(zeros, y0), y1)))) -> c5(MARK(and(tt, and(and(zeros, y0), y1)))) A__LENGTH(cons(z0, and(tt, length(and(and(y0, y1), y2))))) -> c5(MARK(and(tt, length(and(and(y0, y1), y2))))) A__LENGTH(cons(z0, and(tt, length(and(length(y0), y1))))) -> c5(MARK(and(tt, length(and(length(y0), y1))))) A__LENGTH(cons(z0, and(tt, length(and(cons(y0, y1), y2))))) -> c5(MARK(and(tt, length(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, and(tt, length(and(tt, y0))))) -> c5(MARK(and(tt, length(and(tt, y0))))) A__LENGTH(cons(z0, and(tt, length(and(s(y0), y1))))) -> c5(MARK(and(tt, length(and(s(y0), y1))))) A__LENGTH(cons(z0, and(tt, length(and(y0, y1))))) -> c5(MARK(and(tt, length(and(y0, y1))))) A__LENGTH(cons(z0, and(tt, length(and(zeros, y0))))) -> c5(MARK(and(tt, length(and(zeros, y0))))) A__LENGTH(cons(z0, and(tt, length(length(zeros))))) -> c5(MARK(and(tt, length(length(zeros))))) A__LENGTH(cons(z0, and(tt, length(length(and(y0, y1)))))) -> c5(MARK(and(tt, length(length(and(y0, y1)))))) A__LENGTH(cons(z0, and(tt, length(length(length(y0)))))) -> c5(MARK(and(tt, length(length(length(y0)))))) A__LENGTH(cons(z0, and(tt, length(length(cons(y0, y1)))))) -> c5(MARK(and(tt, length(length(cons(y0, y1)))))) A__LENGTH(cons(z0, and(tt, length(length(s(y0)))))) -> c5(MARK(and(tt, length(length(s(y0)))))) A__LENGTH(cons(z0, and(tt, length(length(y0))))) -> c5(MARK(and(tt, length(length(y0))))) A__LENGTH(cons(z0, and(tt, length(zeros)))) -> c5(MARK(and(tt, length(zeros)))) A__LENGTH(cons(z0, and(s(s(y0)), z2))) -> c5(MARK(and(s(s(y0)), z2))) A__LENGTH(cons(z0, and(s(and(cons(y0, y1), y2)), z2))) -> c5(MARK(and(s(and(cons(y0, y1), y2)), z2))) A__LENGTH(cons(z0, and(s(and(tt, y0)), z2))) -> c5(MARK(and(s(and(tt, y0)), z2))) A__LENGTH(cons(z0, and(s(and(s(y0), y1)), z2))) -> c5(MARK(and(s(and(s(y0), y1)), z2))) A__LENGTH(cons(z0, and(s(length(cons(y0, y1))), z2))) -> c5(MARK(and(s(length(cons(y0, y1))), z2))) A__LENGTH(cons(z0, and(s(length(s(y0))), z2))) -> c5(MARK(and(s(length(s(y0))), z2))) A__LENGTH(cons(z0, and(s(and(and(and(y0, y1), y2), y3)), z2))) -> c5(MARK(and(s(and(and(and(y0, y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(and(and(length(y0), y1), y2)), z2))) -> c5(MARK(and(s(and(and(length(y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(and(and(cons(y0, y1), y2), y3)), z2))) -> c5(MARK(and(s(and(and(cons(y0, y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(and(and(tt, y0), y1)), z2))) -> c5(MARK(and(s(and(and(tt, y0), y1)), z2))) A__LENGTH(cons(z0, and(s(and(and(s(y0), y1), y2)), z2))) -> c5(MARK(and(s(and(and(s(y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(and(and(y0, y1), y2)), z2))) -> c5(MARK(and(s(and(and(y0, y1), y2)), z2))) A__LENGTH(cons(z0, and(s(and(length(zeros), y0)), z2))) -> c5(MARK(and(s(and(length(zeros), y0)), z2))) A__LENGTH(cons(z0, and(s(and(length(and(y0, y1)), y2)), z2))) -> c5(MARK(and(s(and(length(and(y0, y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(and(length(length(y0)), y1)), z2))) -> c5(MARK(and(s(and(length(length(y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(and(length(cons(y0, y1)), y2)), z2))) -> c5(MARK(and(s(and(length(cons(y0, y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(and(length(s(y0)), y1)), z2))) -> c5(MARK(and(s(and(length(s(y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(and(length(y0), y1)), z2))) -> c5(MARK(and(s(and(length(y0), y1)), z2))) A__LENGTH(cons(z0, and(s(and(and(zeros, y0), y1)), z2))) -> c5(MARK(and(s(and(and(zeros, y0), y1)), z2))) A__LENGTH(cons(z0, and(s(length(and(and(y0, y1), y2))), z2))) -> c5(MARK(and(s(length(and(and(y0, y1), y2))), z2))) A__LENGTH(cons(z0, and(s(length(and(length(y0), y1))), z2))) -> c5(MARK(and(s(length(and(length(y0), y1))), z2))) A__LENGTH(cons(z0, and(s(length(and(cons(y0, y1), y2))), z2))) -> c5(MARK(and(s(length(and(cons(y0, y1), y2))), z2))) A__LENGTH(cons(z0, and(s(length(and(tt, y0))), z2))) -> c5(MARK(and(s(length(and(tt, y0))), z2))) A__LENGTH(cons(z0, and(s(length(and(s(y0), y1))), z2))) -> c5(MARK(and(s(length(and(s(y0), y1))), z2))) A__LENGTH(cons(z0, and(s(length(and(y0, y1))), z2))) -> c5(MARK(and(s(length(and(y0, y1))), z2))) A__LENGTH(cons(z0, and(s(length(and(zeros, y0))), z2))) -> c5(MARK(and(s(length(and(zeros, y0))), z2))) A__LENGTH(cons(z0, and(s(length(length(zeros))), z2))) -> c5(MARK(and(s(length(length(zeros))), z2))) A__LENGTH(cons(z0, and(s(length(length(and(y0, y1)))), z2))) -> c5(MARK(and(s(length(length(and(y0, y1)))), z2))) A__LENGTH(cons(z0, and(s(length(length(length(y0)))), z2))) -> c5(MARK(and(s(length(length(length(y0)))), z2))) A__LENGTH(cons(z0, and(s(length(length(cons(y0, y1)))), z2))) -> c5(MARK(and(s(length(length(cons(y0, y1)))), z2))) A__LENGTH(cons(z0, and(s(length(length(s(y0)))), z2))) -> c5(MARK(and(s(length(length(s(y0)))), z2))) A__LENGTH(cons(z0, and(s(length(length(y0))), z2))) -> c5(MARK(and(s(length(length(y0))), z2))) A__LENGTH(cons(z0, and(s(length(zeros)), z2))) -> c5(MARK(and(s(length(zeros)), z2))) A__LENGTH(cons(z0, and(s(cons(cons(y0, y1), y2)), z2))) -> c5(MARK(and(s(cons(cons(y0, y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(s(y0), y1)), z2))) -> c5(MARK(and(s(cons(s(y0), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(and(cons(y0, y1), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(cons(y0, y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(tt, y0), y1)), z2))) -> c5(MARK(and(s(cons(and(tt, y0), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(and(s(y0), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(s(y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(cons(y0, y1)), y2)), z2))) -> c5(MARK(and(s(cons(length(cons(y0, y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(s(y0)), y1)), z2))) -> c5(MARK(and(s(cons(length(s(y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(and(y0, y1), y2), y3), y4)), z2))) -> c5(MARK(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(length(y0), y1), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(and(length(y0), y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), z2))) -> c5(MARK(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(tt, y0), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(and(tt, y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(s(y0), y1), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(and(s(y0), y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(y0, y1), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(and(y0, y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(zeros), y0), y1)), z2))) -> c5(MARK(and(s(cons(and(length(zeros), y0), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(and(y0, y1)), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(length(and(y0, y1)), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(length(y0)), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(length(length(y0)), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(cons(y0, y1)), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(length(cons(y0, y1)), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(s(y0)), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(length(s(y0)), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(y0), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(length(y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(zeros, y0), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(and(zeros, y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(and(y0, y1), y2)), y3)), z2))) -> c5(MARK(and(s(cons(length(and(and(y0, y1), y2)), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(length(y0), y1)), y2)), z2))) -> c5(MARK(and(s(cons(length(and(length(y0), y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(cons(y0, y1), y2)), y3)), z2))) -> c5(MARK(and(s(cons(length(and(cons(y0, y1), y2)), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(tt, y0)), y1)), z2))) -> c5(MARK(and(s(cons(length(and(tt, y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(s(y0), y1)), y2)), z2))) -> c5(MARK(and(s(cons(length(and(s(y0), y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(y0, y1)), y2)), z2))) -> c5(MARK(and(s(cons(length(and(y0, y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(zeros, y0)), y1)), z2))) -> c5(MARK(and(s(cons(length(and(zeros, y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(zeros)), y0)), z2))) -> c5(MARK(and(s(cons(length(length(zeros)), y0)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(and(y0, y1))), y2)), z2))) -> c5(MARK(and(s(cons(length(length(and(y0, y1))), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(length(y0))), y1)), z2))) -> c5(MARK(and(s(cons(length(length(length(y0))), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(cons(y0, y1))), y2)), z2))) -> c5(MARK(and(s(cons(length(length(cons(y0, y1))), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(s(y0))), y1)), z2))) -> c5(MARK(and(s(cons(length(length(s(y0))), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(y0)), y1)), z2))) -> c5(MARK(and(s(cons(length(length(y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(zeros), y0)), z2))) -> c5(MARK(and(s(cons(length(zeros), y0)), z2))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__LENGTH_1, MARK_1, A__AND_2 Compound Symbols: c5_2, c9_2, c5_1, c8_2, c8_1, c9_1, c2_1, c10_1, c14_1 ---------------------------------------- (183) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) by A__LENGTH(cons(z0, length(cons(y0, y1)))) -> c5(MARK(length(cons(y0, y1)))) A__LENGTH(cons(z0, length(and(and(y0, y1), y2)))) -> c5(MARK(length(and(and(y0, y1), y2)))) A__LENGTH(cons(z0, length(and(length(y0), y1)))) -> c5(MARK(length(and(length(y0), y1)))) A__LENGTH(cons(z0, length(and(cons(y0, y1), y2)))) -> c5(MARK(length(and(cons(y0, y1), y2)))) A__LENGTH(cons(z0, length(and(tt, y0)))) -> c5(MARK(length(and(tt, y0)))) A__LENGTH(cons(z0, length(and(s(y0), y1)))) -> c5(MARK(length(and(s(y0), y1)))) A__LENGTH(cons(z0, length(and(y0, y1)))) -> c5(MARK(length(and(y0, y1)))) A__LENGTH(cons(z0, length(and(zeros, y0)))) -> c5(MARK(length(and(zeros, y0)))) A__LENGTH(cons(z0, length(length(zeros)))) -> c5(MARK(length(length(zeros)))) A__LENGTH(cons(z0, length(length(and(y0, y1))))) -> c5(MARK(length(length(and(y0, y1))))) A__LENGTH(cons(z0, length(length(length(y0))))) -> c5(MARK(length(length(length(y0))))) A__LENGTH(cons(z0, length(length(cons(y0, y1))))) -> c5(MARK(length(length(cons(y0, y1))))) A__LENGTH(cons(z0, length(length(s(y0))))) -> c5(MARK(length(length(s(y0))))) A__LENGTH(cons(z0, length(length(y0)))) -> c5(MARK(length(length(y0)))) A__LENGTH(cons(z0, length(zeros))) -> c5(MARK(length(zeros))) A__LENGTH(cons(z0, length(s(s(y0))))) -> c5(MARK(length(s(s(y0))))) A__LENGTH(cons(z0, length(s(and(cons(y0, y1), y2))))) -> c5(MARK(length(s(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, length(s(and(tt, y0))))) -> c5(MARK(length(s(and(tt, y0))))) A__LENGTH(cons(z0, length(s(and(s(y0), y1))))) -> c5(MARK(length(s(and(s(y0), y1))))) A__LENGTH(cons(z0, length(s(length(cons(y0, y1)))))) -> c5(MARK(length(s(length(cons(y0, y1)))))) A__LENGTH(cons(z0, length(s(length(s(y0)))))) -> c5(MARK(length(s(length(s(y0)))))) A__LENGTH(cons(z0, length(s(and(and(and(y0, y1), y2), y3))))) -> c5(MARK(length(s(and(and(and(y0, y1), y2), y3))))) A__LENGTH(cons(z0, length(s(and(and(length(y0), y1), y2))))) -> c5(MARK(length(s(and(and(length(y0), y1), y2))))) A__LENGTH(cons(z0, length(s(and(and(cons(y0, y1), y2), y3))))) -> c5(MARK(length(s(and(and(cons(y0, y1), y2), y3))))) A__LENGTH(cons(z0, length(s(and(and(tt, y0), y1))))) -> c5(MARK(length(s(and(and(tt, y0), y1))))) A__LENGTH(cons(z0, length(s(and(and(s(y0), y1), y2))))) -> c5(MARK(length(s(and(and(s(y0), y1), y2))))) A__LENGTH(cons(z0, length(s(and(and(y0, y1), y2))))) -> c5(MARK(length(s(and(and(y0, y1), y2))))) A__LENGTH(cons(z0, length(s(and(length(zeros), y0))))) -> c5(MARK(length(s(and(length(zeros), y0))))) A__LENGTH(cons(z0, length(s(and(length(and(y0, y1)), y2))))) -> c5(MARK(length(s(and(length(and(y0, y1)), y2))))) A__LENGTH(cons(z0, length(s(and(length(length(y0)), y1))))) -> c5(MARK(length(s(and(length(length(y0)), y1))))) A__LENGTH(cons(z0, length(s(and(length(cons(y0, y1)), y2))))) -> c5(MARK(length(s(and(length(cons(y0, y1)), y2))))) A__LENGTH(cons(z0, length(s(and(length(s(y0)), y1))))) -> c5(MARK(length(s(and(length(s(y0)), y1))))) A__LENGTH(cons(z0, length(s(and(length(y0), y1))))) -> c5(MARK(length(s(and(length(y0), y1))))) A__LENGTH(cons(z0, length(s(and(and(zeros, y0), y1))))) -> c5(MARK(length(s(and(and(zeros, y0), y1))))) A__LENGTH(cons(z0, length(s(length(and(and(y0, y1), y2)))))) -> c5(MARK(length(s(length(and(and(y0, y1), y2)))))) A__LENGTH(cons(z0, length(s(length(and(length(y0), y1)))))) -> c5(MARK(length(s(length(and(length(y0), y1)))))) A__LENGTH(cons(z0, length(s(length(and(cons(y0, y1), y2)))))) -> c5(MARK(length(s(length(and(cons(y0, y1), y2)))))) A__LENGTH(cons(z0, length(s(length(and(tt, y0)))))) -> c5(MARK(length(s(length(and(tt, y0)))))) A__LENGTH(cons(z0, length(s(length(and(s(y0), y1)))))) -> c5(MARK(length(s(length(and(s(y0), y1)))))) A__LENGTH(cons(z0, length(s(length(and(y0, y1)))))) -> c5(MARK(length(s(length(and(y0, y1)))))) A__LENGTH(cons(z0, length(s(length(and(zeros, y0)))))) -> c5(MARK(length(s(length(and(zeros, y0)))))) A__LENGTH(cons(z0, length(s(length(length(zeros)))))) -> c5(MARK(length(s(length(length(zeros)))))) A__LENGTH(cons(z0, length(s(length(length(and(y0, y1))))))) -> c5(MARK(length(s(length(length(and(y0, y1))))))) A__LENGTH(cons(z0, length(s(length(length(length(y0))))))) -> c5(MARK(length(s(length(length(length(y0))))))) A__LENGTH(cons(z0, length(s(length(length(cons(y0, y1))))))) -> c5(MARK(length(s(length(length(cons(y0, y1))))))) A__LENGTH(cons(z0, length(s(length(length(s(y0))))))) -> c5(MARK(length(s(length(length(s(y0))))))) A__LENGTH(cons(z0, length(s(length(length(y0)))))) -> c5(MARK(length(s(length(length(y0)))))) A__LENGTH(cons(z0, length(s(length(zeros))))) -> c5(MARK(length(s(length(zeros))))) A__LENGTH(cons(z0, length(s(cons(cons(y0, y1), y2))))) -> c5(MARK(length(s(cons(cons(y0, y1), y2))))) A__LENGTH(cons(z0, length(s(cons(s(y0), y1))))) -> c5(MARK(length(s(cons(s(y0), y1))))) A__LENGTH(cons(z0, length(s(cons(and(cons(y0, y1), y2), y3))))) -> c5(MARK(length(s(cons(and(cons(y0, y1), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(tt, y0), y1))))) -> c5(MARK(length(s(cons(and(tt, y0), y1))))) A__LENGTH(cons(z0, length(s(cons(and(s(y0), y1), y2))))) -> c5(MARK(length(s(cons(and(s(y0), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(length(cons(y0, y1)), y2))))) -> c5(MARK(length(s(cons(length(cons(y0, y1)), y2))))) A__LENGTH(cons(z0, length(s(cons(length(s(y0)), y1))))) -> c5(MARK(length(s(cons(length(s(y0)), y1))))) A__LENGTH(cons(z0, length(s(cons(and(and(and(y0, y1), y2), y3), y4))))) -> c5(MARK(length(s(cons(and(and(and(y0, y1), y2), y3), y4))))) A__LENGTH(cons(z0, length(s(cons(and(and(length(y0), y1), y2), y3))))) -> c5(MARK(length(s(cons(and(and(length(y0), y1), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(and(cons(y0, y1), y2), y3), y4))))) -> c5(MARK(length(s(cons(and(and(cons(y0, y1), y2), y3), y4))))) A__LENGTH(cons(z0, length(s(cons(and(and(tt, y0), y1), y2))))) -> c5(MARK(length(s(cons(and(and(tt, y0), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(and(and(s(y0), y1), y2), y3))))) -> c5(MARK(length(s(cons(and(and(s(y0), y1), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(and(y0, y1), y2), y3))))) -> c5(MARK(length(s(cons(and(and(y0, y1), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(length(zeros), y0), y1))))) -> c5(MARK(length(s(cons(and(length(zeros), y0), y1))))) A__LENGTH(cons(z0, length(s(cons(and(length(and(y0, y1)), y2), y3))))) -> c5(MARK(length(s(cons(and(length(and(y0, y1)), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(length(length(y0)), y1), y2))))) -> c5(MARK(length(s(cons(and(length(length(y0)), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(and(length(cons(y0, y1)), y2), y3))))) -> c5(MARK(length(s(cons(and(length(cons(y0, y1)), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(length(s(y0)), y1), y2))))) -> c5(MARK(length(s(cons(and(length(s(y0)), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(and(length(y0), y1), y2))))) -> c5(MARK(length(s(cons(and(length(y0), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(and(and(zeros, y0), y1), y2))))) -> c5(MARK(length(s(cons(and(and(zeros, y0), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(length(and(and(y0, y1), y2)), y3))))) -> c5(MARK(length(s(cons(length(and(and(y0, y1), y2)), y3))))) A__LENGTH(cons(z0, length(s(cons(length(and(length(y0), y1)), y2))))) -> c5(MARK(length(s(cons(length(and(length(y0), y1)), y2))))) A__LENGTH(cons(z0, length(s(cons(length(and(cons(y0, y1), y2)), y3))))) -> c5(MARK(length(s(cons(length(and(cons(y0, y1), y2)), y3))))) A__LENGTH(cons(z0, length(s(cons(length(and(tt, y0)), y1))))) -> c5(MARK(length(s(cons(length(and(tt, y0)), y1))))) A__LENGTH(cons(z0, length(s(cons(length(and(s(y0), y1)), y2))))) -> c5(MARK(length(s(cons(length(and(s(y0), y1)), y2))))) A__LENGTH(cons(z0, length(s(cons(length(and(y0, y1)), y2))))) -> c5(MARK(length(s(cons(length(and(y0, y1)), y2))))) A__LENGTH(cons(z0, length(s(cons(length(and(zeros, y0)), y1))))) -> c5(MARK(length(s(cons(length(and(zeros, y0)), y1))))) A__LENGTH(cons(z0, length(s(cons(length(length(zeros)), y0))))) -> c5(MARK(length(s(cons(length(length(zeros)), y0))))) A__LENGTH(cons(z0, length(s(cons(length(length(and(y0, y1))), y2))))) -> c5(MARK(length(s(cons(length(length(and(y0, y1))), y2))))) A__LENGTH(cons(z0, length(s(cons(length(length(length(y0))), y1))))) -> c5(MARK(length(s(cons(length(length(length(y0))), y1))))) A__LENGTH(cons(z0, length(s(cons(length(length(cons(y0, y1))), y2))))) -> c5(MARK(length(s(cons(length(length(cons(y0, y1))), y2))))) A__LENGTH(cons(z0, length(s(cons(length(length(s(y0))), y1))))) -> c5(MARK(length(s(cons(length(length(s(y0))), y1))))) A__LENGTH(cons(z0, length(s(cons(length(length(y0)), y1))))) -> c5(MARK(length(s(cons(length(length(y0)), y1))))) A__LENGTH(cons(z0, length(s(cons(length(zeros), y0))))) -> c5(MARK(length(s(cons(length(zeros), y0))))) ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) MARK(cons(and(and(cons(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(cons(y0, y1), y2), y3))) MARK(cons(and(and(tt, y0), y1), z1)) -> c10(MARK(and(and(tt, y0), y1))) MARK(cons(and(and(s(y0), y1), y2), z1)) -> c10(MARK(and(and(s(y0), y1), y2))) MARK(cons(and(and(y0, y1), y2), z1)) -> c10(MARK(and(and(y0, y1), y2))) MARK(cons(and(length(zeros), y0), z1)) -> c10(MARK(and(length(zeros), y0))) MARK(cons(and(length(and(y0, y1)), y2), z1)) -> c10(MARK(and(length(and(y0, y1)), y2))) MARK(cons(and(length(length(y0)), y1), z1)) -> c10(MARK(and(length(length(y0)), y1))) MARK(cons(and(length(cons(y0, y1)), y2), z1)) -> c10(MARK(and(length(cons(y0, y1)), y2))) MARK(cons(and(length(s(y0)), y1), z1)) -> c10(MARK(and(length(s(y0)), y1))) MARK(cons(and(length(y0), y1), z1)) -> c10(MARK(and(length(y0), y1))) MARK(cons(and(and(zeros, y0), y1), z1)) -> c10(MARK(and(and(zeros, y0), y1))) MARK(cons(length(and(and(y0, y1), y2)), z1)) -> c10(MARK(length(and(and(y0, y1), y2)))) MARK(cons(length(and(length(y0), y1)), z1)) -> c10(MARK(length(and(length(y0), y1)))) MARK(cons(length(and(cons(y0, y1), y2)), z1)) -> c10(MARK(length(and(cons(y0, y1), y2)))) MARK(cons(length(and(tt, y0)), z1)) -> c10(MARK(length(and(tt, y0)))) MARK(cons(length(and(s(y0), y1)), z1)) -> c10(MARK(length(and(s(y0), y1)))) MARK(cons(length(and(y0, y1)), z1)) -> c10(MARK(length(and(y0, y1)))) MARK(cons(length(and(zeros, y0)), z1)) -> c10(MARK(length(and(zeros, y0)))) MARK(cons(length(length(zeros)), z1)) -> c10(MARK(length(length(zeros)))) MARK(cons(length(length(and(y0, y1))), z1)) -> c10(MARK(length(length(and(y0, y1))))) MARK(cons(length(length(length(y0))), z1)) -> c10(MARK(length(length(length(y0))))) MARK(cons(length(length(cons(y0, y1))), z1)) -> c10(MARK(length(length(cons(y0, y1))))) MARK(cons(length(length(s(y0))), z1)) -> c10(MARK(length(length(s(y0))))) MARK(cons(length(length(y0)), z1)) -> c10(MARK(length(length(y0)))) MARK(cons(length(zeros), z1)) -> c10(MARK(length(zeros))) MARK(s(s(y0))) -> c14(MARK(s(y0))) MARK(s(and(cons(y0, y1), y2))) -> c14(MARK(and(cons(y0, y1), y2))) MARK(s(and(tt, y0))) -> c14(MARK(and(tt, y0))) MARK(s(and(s(y0), y1))) -> c14(MARK(and(s(y0), y1))) MARK(s(length(cons(y0, y1)))) -> c14(MARK(length(cons(y0, y1)))) MARK(s(length(s(y0)))) -> c14(MARK(length(s(y0)))) MARK(s(and(and(and(y0, y1), y2), y3))) -> c14(MARK(and(and(and(y0, y1), y2), y3))) MARK(s(and(and(length(y0), y1), y2))) -> c14(MARK(and(and(length(y0), y1), y2))) MARK(s(and(and(cons(y0, y1), y2), y3))) -> c14(MARK(and(and(cons(y0, y1), y2), y3))) MARK(s(and(and(tt, y0), y1))) -> c14(MARK(and(and(tt, y0), y1))) MARK(s(and(and(s(y0), y1), y2))) -> c14(MARK(and(and(s(y0), y1), y2))) MARK(s(and(and(y0, y1), y2))) -> c14(MARK(and(and(y0, y1), y2))) MARK(s(and(length(zeros), y0))) -> c14(MARK(and(length(zeros), y0))) MARK(s(and(length(and(y0, y1)), y2))) -> c14(MARK(and(length(and(y0, y1)), y2))) MARK(s(and(length(length(y0)), y1))) -> c14(MARK(and(length(length(y0)), y1))) MARK(s(and(length(cons(y0, y1)), y2))) -> c14(MARK(and(length(cons(y0, y1)), y2))) MARK(s(and(length(s(y0)), y1))) -> c14(MARK(and(length(s(y0)), y1))) MARK(s(and(length(y0), y1))) -> c14(MARK(and(length(y0), y1))) MARK(s(and(and(zeros, y0), y1))) -> c14(MARK(and(and(zeros, y0), y1))) MARK(s(length(and(and(y0, y1), y2)))) -> c14(MARK(length(and(and(y0, y1), y2)))) MARK(s(length(and(length(y0), y1)))) -> c14(MARK(length(and(length(y0), y1)))) MARK(s(length(and(cons(y0, y1), y2)))) -> c14(MARK(length(and(cons(y0, y1), y2)))) MARK(s(length(and(tt, y0)))) -> c14(MARK(length(and(tt, y0)))) MARK(s(length(and(s(y0), y1)))) -> c14(MARK(length(and(s(y0), y1)))) MARK(s(length(and(y0, y1)))) -> c14(MARK(length(and(y0, y1)))) MARK(s(length(and(zeros, y0)))) -> c14(MARK(length(and(zeros, y0)))) MARK(s(length(length(zeros)))) -> c14(MARK(length(length(zeros)))) MARK(s(length(length(and(y0, y1))))) -> c14(MARK(length(length(and(y0, y1))))) MARK(s(length(length(length(y0))))) -> c14(MARK(length(length(length(y0))))) MARK(s(length(length(cons(y0, y1))))) -> c14(MARK(length(length(cons(y0, y1))))) MARK(s(length(length(s(y0))))) -> c14(MARK(length(length(s(y0))))) MARK(s(length(length(y0)))) -> c14(MARK(length(length(y0)))) MARK(s(length(zeros))) -> c14(MARK(length(zeros))) MARK(s(cons(cons(y0, y1), y2))) -> c14(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c14(MARK(cons(s(y0), y1))) MARK(s(cons(and(cons(y0, y1), y2), y3))) -> c14(MARK(cons(and(cons(y0, y1), y2), y3))) MARK(s(cons(and(tt, y0), y1))) -> c14(MARK(cons(and(tt, y0), y1))) MARK(s(cons(and(s(y0), y1), y2))) -> c14(MARK(cons(and(s(y0), y1), y2))) MARK(s(cons(length(cons(y0, y1)), y2))) -> c14(MARK(cons(length(cons(y0, y1)), y2))) MARK(s(cons(length(s(y0)), y1))) -> c14(MARK(cons(length(s(y0)), y1))) MARK(s(cons(and(and(and(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(and(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(length(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(length(y0), y1), y2), y3))) MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(cons(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(tt, y0), y1), y2))) -> c14(MARK(cons(and(and(tt, y0), y1), y2))) MARK(s(cons(and(and(s(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(s(y0), y1), y2), y3))) MARK(s(cons(and(and(y0, y1), y2), y3))) -> c14(MARK(cons(and(and(y0, y1), y2), y3))) MARK(s(cons(and(length(zeros), y0), y1))) -> c14(MARK(cons(and(length(zeros), y0), y1))) MARK(s(cons(and(length(and(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(and(y0, y1)), y2), y3))) MARK(s(cons(and(length(length(y0)), y1), y2))) -> c14(MARK(cons(and(length(length(y0)), y1), y2))) MARK(s(cons(and(length(cons(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(cons(y0, y1)), y2), y3))) MARK(s(cons(and(length(s(y0)), y1), y2))) -> c14(MARK(cons(and(length(s(y0)), y1), y2))) MARK(s(cons(and(length(y0), y1), y2))) -> c14(MARK(cons(and(length(y0), y1), y2))) MARK(s(cons(and(and(zeros, y0), y1), y2))) -> c14(MARK(cons(and(and(zeros, y0), y1), y2))) MARK(s(cons(length(and(and(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(and(y0, y1), y2)), y3))) MARK(s(cons(length(and(length(y0), y1)), y2))) -> c14(MARK(cons(length(and(length(y0), y1)), y2))) MARK(s(cons(length(and(cons(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(cons(y0, y1), y2)), y3))) MARK(s(cons(length(and(tt, y0)), y1))) -> c14(MARK(cons(length(and(tt, y0)), y1))) MARK(s(cons(length(and(s(y0), y1)), y2))) -> c14(MARK(cons(length(and(s(y0), y1)), y2))) MARK(s(cons(length(and(y0, y1)), y2))) -> c14(MARK(cons(length(and(y0, y1)), y2))) MARK(s(cons(length(and(zeros, y0)), y1))) -> c14(MARK(cons(length(and(zeros, y0)), y1))) MARK(s(cons(length(length(zeros)), y0))) -> c14(MARK(cons(length(length(zeros)), y0))) MARK(s(cons(length(length(and(y0, y1))), y2))) -> c14(MARK(cons(length(length(and(y0, y1))), y2))) MARK(s(cons(length(length(length(y0))), y1))) -> c14(MARK(cons(length(length(length(y0))), y1))) MARK(s(cons(length(length(cons(y0, y1))), y2))) -> c14(MARK(cons(length(length(cons(y0, y1))), y2))) MARK(s(cons(length(length(s(y0))), y1))) -> c14(MARK(cons(length(length(s(y0))), y1))) MARK(s(cons(length(length(y0)), y1))) -> c14(MARK(cons(length(length(y0)), y1))) MARK(s(cons(length(zeros), y0))) -> c14(MARK(cons(length(zeros), y0))) A__LENGTH(cons(z0, s(s(y0)))) -> c5(MARK(s(s(y0)))) A__LENGTH(cons(z0, s(and(cons(y0, y1), y2)))) -> c5(MARK(s(and(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(tt, y0)))) -> c5(MARK(s(and(tt, y0)))) A__LENGTH(cons(z0, s(and(s(y0), y1)))) -> c5(MARK(s(and(s(y0), y1)))) A__LENGTH(cons(z0, s(length(cons(y0, y1))))) -> c5(MARK(s(length(cons(y0, y1))))) A__LENGTH(cons(z0, s(length(s(y0))))) -> c5(MARK(s(length(s(y0))))) A__LENGTH(cons(z0, s(and(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(length(y0), y1), y2)))) -> c5(MARK(s(and(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(tt, y0), y1)))) -> c5(MARK(s(and(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(and(and(s(y0), y1), y2)))) -> c5(MARK(s(and(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(y0, y1), y2)))) -> c5(MARK(s(and(and(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(length(zeros), y0)))) -> c5(MARK(s(and(length(zeros), y0)))) A__LENGTH(cons(z0, s(and(length(and(y0, y1)), y2)))) -> c5(MARK(s(and(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(length(y0)), y1)))) -> c5(MARK(s(and(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(cons(y0, y1)), y2)))) -> c5(MARK(s(and(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(s(y0)), y1)))) -> c5(MARK(s(and(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(y0), y1)))) -> c5(MARK(s(and(length(y0), y1)))) A__LENGTH(cons(z0, s(and(and(zeros, y0), y1)))) -> c5(MARK(s(and(and(zeros, y0), y1)))) A__LENGTH(cons(z0, s(length(and(and(y0, y1), y2))))) -> c5(MARK(s(length(and(and(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(length(y0), y1))))) -> c5(MARK(s(length(and(length(y0), y1))))) A__LENGTH(cons(z0, s(length(and(cons(y0, y1), y2))))) -> c5(MARK(s(length(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(tt, y0))))) -> c5(MARK(s(length(and(tt, y0))))) A__LENGTH(cons(z0, s(length(and(s(y0), y1))))) -> c5(MARK(s(length(and(s(y0), y1))))) A__LENGTH(cons(z0, s(length(and(y0, y1))))) -> c5(MARK(s(length(and(y0, y1))))) A__LENGTH(cons(z0, s(length(and(zeros, y0))))) -> c5(MARK(s(length(and(zeros, y0))))) A__LENGTH(cons(z0, s(length(length(zeros))))) -> c5(MARK(s(length(length(zeros))))) A__LENGTH(cons(z0, s(length(length(and(y0, y1)))))) -> c5(MARK(s(length(length(and(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(length(y0)))))) -> c5(MARK(s(length(length(length(y0)))))) A__LENGTH(cons(z0, s(length(length(cons(y0, y1)))))) -> c5(MARK(s(length(length(cons(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(s(y0)))))) -> c5(MARK(s(length(length(s(y0)))))) A__LENGTH(cons(z0, s(length(length(y0))))) -> c5(MARK(s(length(length(y0))))) A__LENGTH(cons(z0, s(length(zeros)))) -> c5(MARK(s(length(zeros)))) A__LENGTH(cons(z0, s(cons(cons(y0, y1), y2)))) -> c5(MARK(s(cons(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(cons(s(y0), y1)))) -> c5(MARK(s(cons(s(y0), y1)))) A__LENGTH(cons(z0, s(cons(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(tt, y0), y1)))) -> c5(MARK(s(cons(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(cons(and(s(y0), y1), y2)))) -> c5(MARK(s(cons(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(length(cons(y0, y1)), y2)))) -> c5(MARK(s(cons(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(s(y0)), y1)))) -> c5(MARK(s(cons(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(cons(and(and(and(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(and(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(length(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(length(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(cons(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(tt, y0), y1), y2)))) -> c5(MARK(s(cons(and(and(tt, y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(and(s(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(s(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(and(y0, y1), y2), y3)))) 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-> c5(MARK(and(s(and(tt, y0)), z2))) A__LENGTH(cons(z0, and(s(and(s(y0), y1)), z2))) -> c5(MARK(and(s(and(s(y0), y1)), z2))) A__LENGTH(cons(z0, and(s(length(cons(y0, y1))), z2))) -> c5(MARK(and(s(length(cons(y0, y1))), z2))) A__LENGTH(cons(z0, and(s(length(s(y0))), z2))) -> c5(MARK(and(s(length(s(y0))), z2))) A__LENGTH(cons(z0, and(s(and(and(and(y0, y1), y2), y3)), z2))) -> c5(MARK(and(s(and(and(and(y0, y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(and(and(length(y0), y1), y2)), z2))) -> c5(MARK(and(s(and(and(length(y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(and(and(cons(y0, y1), y2), y3)), z2))) -> c5(MARK(and(s(and(and(cons(y0, y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(and(and(tt, y0), y1)), z2))) -> c5(MARK(and(s(and(and(tt, y0), y1)), z2))) A__LENGTH(cons(z0, and(s(and(and(s(y0), y1), y2)), z2))) -> c5(MARK(and(s(and(and(s(y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(and(and(y0, y1), y2)), z2))) -> c5(MARK(and(s(and(and(y0, y1), y2)), z2))) A__LENGTH(cons(z0, and(s(and(length(zeros), y0)), z2))) -> c5(MARK(and(s(and(length(zeros), y0)), z2))) A__LENGTH(cons(z0, and(s(and(length(and(y0, y1)), y2)), z2))) -> c5(MARK(and(s(and(length(and(y0, y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(and(length(length(y0)), y1)), z2))) -> c5(MARK(and(s(and(length(length(y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(and(length(cons(y0, y1)), y2)), z2))) -> c5(MARK(and(s(and(length(cons(y0, y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(and(length(s(y0)), y1)), z2))) -> c5(MARK(and(s(and(length(s(y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(and(length(y0), y1)), z2))) -> c5(MARK(and(s(and(length(y0), y1)), z2))) A__LENGTH(cons(z0, and(s(and(and(zeros, y0), y1)), z2))) -> c5(MARK(and(s(and(and(zeros, y0), y1)), z2))) A__LENGTH(cons(z0, and(s(length(and(and(y0, y1), y2))), z2))) -> c5(MARK(and(s(length(and(and(y0, y1), y2))), z2))) A__LENGTH(cons(z0, and(s(length(and(length(y0), y1))), z2))) -> c5(MARK(and(s(length(and(length(y0), y1))), z2))) A__LENGTH(cons(z0, 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z2))) -> c5(MARK(and(s(length(length(s(y0)))), z2))) A__LENGTH(cons(z0, and(s(length(length(y0))), z2))) -> c5(MARK(and(s(length(length(y0))), z2))) A__LENGTH(cons(z0, and(s(length(zeros)), z2))) -> c5(MARK(and(s(length(zeros)), z2))) A__LENGTH(cons(z0, and(s(cons(cons(y0, y1), y2)), z2))) -> c5(MARK(and(s(cons(cons(y0, y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(s(y0), y1)), z2))) -> c5(MARK(and(s(cons(s(y0), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(and(cons(y0, y1), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(cons(y0, y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(tt, y0), y1)), z2))) -> c5(MARK(and(s(cons(and(tt, y0), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(and(s(y0), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(s(y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(cons(y0, y1)), y2)), z2))) -> c5(MARK(and(s(cons(length(cons(y0, y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(s(y0)), y1)), z2))) -> c5(MARK(and(s(cons(length(s(y0)), y1)), z2))) 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c5(MARK(and(s(cons(and(length(and(y0, y1)), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(length(y0)), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(length(length(y0)), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(cons(y0, y1)), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(length(cons(y0, y1)), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(s(y0)), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(length(s(y0)), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(y0), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(length(y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(zeros, y0), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(and(zeros, y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(and(y0, y1), y2)), y3)), z2))) -> c5(MARK(and(s(cons(length(and(and(y0, y1), y2)), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(length(y0), y1)), y2)), z2))) -> c5(MARK(and(s(cons(length(and(length(y0), y1)), y2)), z2))) A__LENGTH(cons(z0, 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A__LENGTH(cons(z0, and(s(cons(length(length(cons(y0, y1))), y2)), z2))) -> c5(MARK(and(s(cons(length(length(cons(y0, y1))), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(s(y0))), y1)), z2))) -> c5(MARK(and(s(cons(length(length(s(y0))), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(y0)), y1)), z2))) -> c5(MARK(and(s(cons(length(length(y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(zeros), y0)), z2))) -> c5(MARK(and(s(cons(length(zeros), y0)), z2))) A__LENGTH(cons(z0, length(cons(y0, y1)))) -> c5(MARK(length(cons(y0, y1)))) A__LENGTH(cons(z0, length(and(and(y0, y1), y2)))) -> c5(MARK(length(and(and(y0, y1), y2)))) A__LENGTH(cons(z0, length(and(length(y0), y1)))) -> c5(MARK(length(and(length(y0), y1)))) A__LENGTH(cons(z0, length(and(cons(y0, y1), y2)))) -> c5(MARK(length(and(cons(y0, y1), y2)))) A__LENGTH(cons(z0, length(and(tt, y0)))) -> c5(MARK(length(and(tt, y0)))) A__LENGTH(cons(z0, length(and(s(y0), y1)))) -> c5(MARK(length(and(s(y0), y1)))) A__LENGTH(cons(z0, length(and(y0, y1)))) -> c5(MARK(length(and(y0, y1)))) A__LENGTH(cons(z0, length(and(zeros, y0)))) -> c5(MARK(length(and(zeros, y0)))) A__LENGTH(cons(z0, length(length(zeros)))) -> c5(MARK(length(length(zeros)))) A__LENGTH(cons(z0, length(length(and(y0, y1))))) -> c5(MARK(length(length(and(y0, y1))))) A__LENGTH(cons(z0, length(length(length(y0))))) -> c5(MARK(length(length(length(y0))))) A__LENGTH(cons(z0, length(length(cons(y0, y1))))) -> c5(MARK(length(length(cons(y0, y1))))) A__LENGTH(cons(z0, length(length(s(y0))))) -> c5(MARK(length(length(s(y0))))) A__LENGTH(cons(z0, length(length(y0)))) -> c5(MARK(length(length(y0)))) A__LENGTH(cons(z0, length(zeros))) -> c5(MARK(length(zeros))) A__LENGTH(cons(z0, length(s(s(y0))))) -> c5(MARK(length(s(s(y0))))) A__LENGTH(cons(z0, length(s(and(cons(y0, y1), y2))))) -> c5(MARK(length(s(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, length(s(and(tt, y0))))) -> c5(MARK(length(s(and(tt, y0))))) A__LENGTH(cons(z0, length(s(and(s(y0), 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A__LENGTH(cons(z0, length(s(cons(and(and(length(y0), y1), y2), y3))))) -> c5(MARK(length(s(cons(and(and(length(y0), y1), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(and(cons(y0, y1), y2), y3), y4))))) -> c5(MARK(length(s(cons(and(and(cons(y0, y1), y2), y3), y4))))) A__LENGTH(cons(z0, length(s(cons(and(and(tt, y0), y1), y2))))) -> c5(MARK(length(s(cons(and(and(tt, y0), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(and(and(s(y0), y1), y2), y3))))) -> c5(MARK(length(s(cons(and(and(s(y0), y1), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(and(y0, y1), y2), y3))))) -> c5(MARK(length(s(cons(and(and(y0, y1), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(length(zeros), y0), y1))))) -> c5(MARK(length(s(cons(and(length(zeros), y0), y1))))) A__LENGTH(cons(z0, length(s(cons(and(length(and(y0, y1)), y2), y3))))) -> c5(MARK(length(s(cons(and(length(and(y0, y1)), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(length(length(y0)), y1), y2))))) -> c5(MARK(length(s(cons(and(length(length(y0)), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(and(length(cons(y0, y1)), y2), y3))))) -> c5(MARK(length(s(cons(and(length(cons(y0, y1)), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(length(s(y0)), y1), y2))))) -> c5(MARK(length(s(cons(and(length(s(y0)), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(and(length(y0), y1), y2))))) -> c5(MARK(length(s(cons(and(length(y0), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(and(and(zeros, y0), y1), y2))))) -> c5(MARK(length(s(cons(and(and(zeros, y0), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(length(and(and(y0, y1), y2)), y3))))) -> c5(MARK(length(s(cons(length(and(and(y0, y1), y2)), y3))))) A__LENGTH(cons(z0, length(s(cons(length(and(length(y0), y1)), y2))))) -> c5(MARK(length(s(cons(length(and(length(y0), y1)), y2))))) A__LENGTH(cons(z0, length(s(cons(length(and(cons(y0, y1), y2)), y3))))) -> c5(MARK(length(s(cons(length(and(cons(y0, y1), y2)), y3))))) A__LENGTH(cons(z0, length(s(cons(length(and(tt, y0)), y1))))) -> c5(MARK(length(s(cons(length(and(tt, y0)), y1))))) A__LENGTH(cons(z0, length(s(cons(length(and(s(y0), y1)), y2))))) -> c5(MARK(length(s(cons(length(and(s(y0), y1)), y2))))) A__LENGTH(cons(z0, length(s(cons(length(and(y0, y1)), y2))))) -> c5(MARK(length(s(cons(length(and(y0, y1)), y2))))) A__LENGTH(cons(z0, length(s(cons(length(and(zeros, y0)), y1))))) -> c5(MARK(length(s(cons(length(and(zeros, y0)), y1))))) A__LENGTH(cons(z0, length(s(cons(length(length(zeros)), y0))))) -> c5(MARK(length(s(cons(length(length(zeros)), y0))))) A__LENGTH(cons(z0, length(s(cons(length(length(and(y0, y1))), y2))))) -> c5(MARK(length(s(cons(length(length(and(y0, y1))), y2))))) A__LENGTH(cons(z0, length(s(cons(length(length(length(y0))), y1))))) -> c5(MARK(length(s(cons(length(length(length(y0))), y1))))) A__LENGTH(cons(z0, length(s(cons(length(length(cons(y0, y1))), y2))))) -> c5(MARK(length(s(cons(length(length(cons(y0, y1))), y2))))) A__LENGTH(cons(z0, length(s(cons(length(length(s(y0))), y1))))) -> c5(MARK(length(s(cons(length(length(s(y0))), y1))))) A__LENGTH(cons(z0, length(s(cons(length(length(y0)), y1))))) -> c5(MARK(length(s(cons(length(length(y0)), y1))))) A__LENGTH(cons(z0, length(s(cons(length(zeros), y0))))) -> c5(MARK(length(s(cons(length(zeros), y0))))) S tuples: A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) MARK(cons(and(and(cons(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(cons(y0, y1), y2), y3))) MARK(cons(and(and(tt, y0), y1), z1)) -> c10(MARK(and(and(tt, y0), y1))) MARK(cons(and(and(s(y0), y1), y2), z1)) -> c10(MARK(and(and(s(y0), y1), y2))) MARK(cons(and(and(y0, y1), y2), z1)) -> c10(MARK(and(and(y0, y1), y2))) MARK(cons(and(length(zeros), y0), z1)) -> c10(MARK(and(length(zeros), y0))) MARK(cons(and(length(and(y0, y1)), y2), z1)) -> c10(MARK(and(length(and(y0, y1)), y2))) MARK(cons(and(length(length(y0)), y1), z1)) -> c10(MARK(and(length(length(y0)), y1))) MARK(cons(and(length(cons(y0, y1)), y2), z1)) -> c10(MARK(and(length(cons(y0, y1)), y2))) MARK(cons(and(length(s(y0)), y1), z1)) -> c10(MARK(and(length(s(y0)), y1))) MARK(cons(and(length(y0), y1), z1)) -> c10(MARK(and(length(y0), y1))) MARK(cons(and(and(zeros, y0), y1), z1)) -> c10(MARK(and(and(zeros, y0), y1))) MARK(cons(length(and(and(y0, y1), y2)), z1)) -> c10(MARK(length(and(and(y0, y1), y2)))) MARK(cons(length(and(length(y0), y1)), z1)) -> c10(MARK(length(and(length(y0), y1)))) MARK(cons(length(and(cons(y0, y1), y2)), z1)) -> c10(MARK(length(and(cons(y0, y1), y2)))) MARK(cons(length(and(tt, y0)), z1)) -> c10(MARK(length(and(tt, y0)))) MARK(cons(length(and(s(y0), y1)), z1)) -> c10(MARK(length(and(s(y0), y1)))) MARK(cons(length(and(y0, y1)), z1)) -> c10(MARK(length(and(y0, y1)))) MARK(cons(length(and(zeros, y0)), z1)) -> c10(MARK(length(and(zeros, y0)))) MARK(cons(length(length(zeros)), z1)) -> c10(MARK(length(length(zeros)))) MARK(cons(length(length(and(y0, y1))), z1)) -> c10(MARK(length(length(and(y0, y1))))) MARK(cons(length(length(length(y0))), z1)) -> c10(MARK(length(length(length(y0))))) MARK(cons(length(length(cons(y0, y1))), z1)) -> c10(MARK(length(length(cons(y0, y1))))) MARK(cons(length(length(s(y0))), z1)) -> c10(MARK(length(length(s(y0))))) MARK(cons(length(length(y0)), z1)) -> c10(MARK(length(length(y0)))) MARK(cons(length(zeros), z1)) -> c10(MARK(length(zeros))) MARK(s(s(y0))) -> c14(MARK(s(y0))) MARK(s(and(cons(y0, y1), y2))) -> c14(MARK(and(cons(y0, y1), y2))) MARK(s(and(tt, y0))) -> c14(MARK(and(tt, y0))) MARK(s(and(s(y0), y1))) -> c14(MARK(and(s(y0), y1))) MARK(s(length(cons(y0, y1)))) -> c14(MARK(length(cons(y0, y1)))) MARK(s(length(s(y0)))) -> c14(MARK(length(s(y0)))) MARK(s(and(and(and(y0, y1), y2), y3))) -> c14(MARK(and(and(and(y0, y1), y2), y3))) MARK(s(and(and(length(y0), y1), y2))) -> c14(MARK(and(and(length(y0), y1), y2))) MARK(s(and(and(cons(y0, y1), y2), y3))) -> c14(MARK(and(and(cons(y0, y1), y2), y3))) MARK(s(and(and(tt, y0), y1))) -> c14(MARK(and(and(tt, y0), y1))) MARK(s(and(and(s(y0), y1), y2))) -> c14(MARK(and(and(s(y0), y1), y2))) MARK(s(and(and(y0, y1), y2))) -> c14(MARK(and(and(y0, y1), y2))) MARK(s(and(length(zeros), y0))) -> c14(MARK(and(length(zeros), y0))) MARK(s(and(length(and(y0, y1)), y2))) -> c14(MARK(and(length(and(y0, y1)), y2))) MARK(s(and(length(length(y0)), y1))) -> c14(MARK(and(length(length(y0)), y1))) MARK(s(and(length(cons(y0, y1)), y2))) -> c14(MARK(and(length(cons(y0, y1)), y2))) MARK(s(and(length(s(y0)), y1))) -> c14(MARK(and(length(s(y0)), y1))) MARK(s(and(length(y0), y1))) -> c14(MARK(and(length(y0), y1))) MARK(s(and(and(zeros, y0), y1))) -> c14(MARK(and(and(zeros, y0), y1))) MARK(s(length(and(and(y0, y1), y2)))) -> c14(MARK(length(and(and(y0, y1), y2)))) MARK(s(length(and(length(y0), y1)))) -> c14(MARK(length(and(length(y0), y1)))) MARK(s(length(and(cons(y0, y1), y2)))) -> c14(MARK(length(and(cons(y0, y1), y2)))) MARK(s(length(and(tt, y0)))) -> c14(MARK(length(and(tt, y0)))) MARK(s(length(and(s(y0), y1)))) -> c14(MARK(length(and(s(y0), y1)))) MARK(s(length(and(y0, y1)))) -> c14(MARK(length(and(y0, y1)))) MARK(s(length(and(zeros, y0)))) -> c14(MARK(length(and(zeros, y0)))) MARK(s(length(length(zeros)))) -> c14(MARK(length(length(zeros)))) MARK(s(length(length(and(y0, y1))))) -> c14(MARK(length(length(and(y0, y1))))) MARK(s(length(length(length(y0))))) -> c14(MARK(length(length(length(y0))))) MARK(s(length(length(cons(y0, y1))))) -> c14(MARK(length(length(cons(y0, y1))))) MARK(s(length(length(s(y0))))) -> c14(MARK(length(length(s(y0))))) MARK(s(length(length(y0)))) -> c14(MARK(length(length(y0)))) MARK(s(length(zeros))) -> c14(MARK(length(zeros))) MARK(s(cons(cons(y0, y1), y2))) -> c14(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c14(MARK(cons(s(y0), y1))) MARK(s(cons(and(cons(y0, y1), y2), y3))) -> c14(MARK(cons(and(cons(y0, y1), y2), y3))) MARK(s(cons(and(tt, y0), y1))) -> c14(MARK(cons(and(tt, y0), y1))) MARK(s(cons(and(s(y0), y1), y2))) -> c14(MARK(cons(and(s(y0), y1), y2))) MARK(s(cons(length(cons(y0, y1)), y2))) -> c14(MARK(cons(length(cons(y0, y1)), y2))) MARK(s(cons(length(s(y0)), y1))) -> c14(MARK(cons(length(s(y0)), y1))) 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y2))) -> c14(MARK(cons(and(length(s(y0)), y1), y2))) MARK(s(cons(and(length(y0), y1), y2))) -> c14(MARK(cons(and(length(y0), y1), y2))) MARK(s(cons(and(and(zeros, y0), y1), y2))) -> c14(MARK(cons(and(and(zeros, y0), y1), y2))) MARK(s(cons(length(and(and(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(and(y0, y1), y2)), y3))) MARK(s(cons(length(and(length(y0), y1)), y2))) -> c14(MARK(cons(length(and(length(y0), y1)), y2))) MARK(s(cons(length(and(cons(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(cons(y0, y1), y2)), y3))) MARK(s(cons(length(and(tt, y0)), y1))) -> c14(MARK(cons(length(and(tt, y0)), y1))) MARK(s(cons(length(and(s(y0), y1)), y2))) -> c14(MARK(cons(length(and(s(y0), y1)), y2))) MARK(s(cons(length(and(y0, y1)), y2))) -> c14(MARK(cons(length(and(y0, y1)), y2))) MARK(s(cons(length(and(zeros, y0)), y1))) -> c14(MARK(cons(length(and(zeros, y0)), y1))) MARK(s(cons(length(length(zeros)), y0))) -> c14(MARK(cons(length(length(zeros)), y0))) MARK(s(cons(length(length(and(y0, 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c8(MARK(s(cons(length(cons(y0, y1)), y2)))) MARK(and(s(cons(length(s(y0)), y1)), z1)) -> c8(MARK(s(cons(length(s(y0)), y1)))) MARK(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), z1)) -> c8(MARK(s(cons(and(and(and(y0, y1), y2), y3), y4)))) MARK(and(s(cons(and(and(length(y0), y1), y2), y3)), z1)) -> c8(MARK(s(cons(and(and(length(y0), y1), y2), y3)))) MARK(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), z1)) -> c8(MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) MARK(and(s(cons(and(and(tt, y0), y1), y2)), z1)) -> c8(MARK(s(cons(and(and(tt, y0), y1), y2)))) MARK(and(s(cons(and(and(s(y0), y1), y2), y3)), z1)) -> c8(MARK(s(cons(and(and(s(y0), y1), y2), y3)))) MARK(and(s(cons(and(and(y0, y1), y2), y3)), z1)) -> c8(MARK(s(cons(and(and(y0, y1), y2), y3)))) MARK(and(s(cons(and(length(zeros), y0), y1)), z1)) -> c8(MARK(s(cons(and(length(zeros), y0), y1)))) MARK(and(s(cons(and(length(and(y0, y1)), y2), y3)), z1)) -> c8(MARK(s(cons(and(length(and(y0, y1)), y2), y3)))) 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-> c8(MARK(s(cons(length(and(s(y0), y1)), y2)))) MARK(and(s(cons(length(and(y0, y1)), y2)), z1)) -> c8(MARK(s(cons(length(and(y0, y1)), y2)))) MARK(and(s(cons(length(and(zeros, y0)), y1)), z1)) -> c8(MARK(s(cons(length(and(zeros, y0)), y1)))) MARK(and(s(cons(length(length(zeros)), y0)), z1)) -> c8(MARK(s(cons(length(length(zeros)), y0)))) MARK(and(s(cons(length(length(and(y0, y1))), y2)), z1)) -> c8(MARK(s(cons(length(length(and(y0, y1))), y2)))) MARK(and(s(cons(length(length(length(y0))), y1)), z1)) -> c8(MARK(s(cons(length(length(length(y0))), y1)))) MARK(and(s(cons(length(length(cons(y0, y1))), y2)), z1)) -> c8(MARK(s(cons(length(length(cons(y0, y1))), y2)))) MARK(and(s(cons(length(length(s(y0))), y1)), z1)) -> c8(MARK(s(cons(length(length(s(y0))), y1)))) MARK(and(s(cons(length(length(y0)), y1)), z1)) -> c8(MARK(s(cons(length(length(y0)), y1)))) MARK(and(s(cons(length(zeros), y0)), z1)) -> c8(MARK(s(cons(length(zeros), y0)))) MARK(length(s(s(y0)))) -> c9(MARK(s(s(y0)))) 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A__LENGTH(cons(z0, and(s(cons(length(and(y0, y1)), y2)), z2))) -> c5(MARK(and(s(cons(length(and(y0, y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(zeros, y0)), y1)), z2))) -> c5(MARK(and(s(cons(length(and(zeros, y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(zeros)), y0)), z2))) -> c5(MARK(and(s(cons(length(length(zeros)), y0)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(and(y0, y1))), y2)), z2))) -> c5(MARK(and(s(cons(length(length(and(y0, y1))), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(length(y0))), y1)), z2))) -> c5(MARK(and(s(cons(length(length(length(y0))), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(cons(y0, y1))), y2)), z2))) -> c5(MARK(and(s(cons(length(length(cons(y0, y1))), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(s(y0))), y1)), z2))) -> c5(MARK(and(s(cons(length(length(s(y0))), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(y0)), y1)), z2))) -> c5(MARK(and(s(cons(length(length(y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(zeros), y0)), z2))) -> c5(MARK(and(s(cons(length(zeros), y0)), z2))) A__LENGTH(cons(z0, length(cons(y0, y1)))) -> c5(MARK(length(cons(y0, y1)))) A__LENGTH(cons(z0, length(and(and(y0, y1), y2)))) -> c5(MARK(length(and(and(y0, y1), y2)))) A__LENGTH(cons(z0, length(and(length(y0), y1)))) -> c5(MARK(length(and(length(y0), y1)))) A__LENGTH(cons(z0, length(and(cons(y0, y1), y2)))) -> c5(MARK(length(and(cons(y0, y1), y2)))) A__LENGTH(cons(z0, length(and(tt, y0)))) -> c5(MARK(length(and(tt, y0)))) A__LENGTH(cons(z0, length(and(s(y0), y1)))) -> c5(MARK(length(and(s(y0), y1)))) A__LENGTH(cons(z0, length(and(y0, y1)))) -> c5(MARK(length(and(y0, y1)))) A__LENGTH(cons(z0, length(and(zeros, y0)))) -> c5(MARK(length(and(zeros, y0)))) A__LENGTH(cons(z0, length(length(zeros)))) -> c5(MARK(length(length(zeros)))) A__LENGTH(cons(z0, length(length(and(y0, y1))))) -> c5(MARK(length(length(and(y0, y1))))) A__LENGTH(cons(z0, length(length(length(y0))))) -> c5(MARK(length(length(length(y0))))) A__LENGTH(cons(z0, length(length(cons(y0, y1))))) -> c5(MARK(length(length(cons(y0, y1))))) A__LENGTH(cons(z0, length(length(s(y0))))) -> c5(MARK(length(length(s(y0))))) A__LENGTH(cons(z0, length(length(y0)))) -> c5(MARK(length(length(y0)))) A__LENGTH(cons(z0, length(zeros))) -> c5(MARK(length(zeros))) A__LENGTH(cons(z0, length(s(s(y0))))) -> c5(MARK(length(s(s(y0))))) A__LENGTH(cons(z0, length(s(and(cons(y0, y1), y2))))) -> c5(MARK(length(s(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, length(s(and(tt, y0))))) -> c5(MARK(length(s(and(tt, y0))))) A__LENGTH(cons(z0, length(s(and(s(y0), y1))))) -> c5(MARK(length(s(and(s(y0), y1))))) A__LENGTH(cons(z0, length(s(length(cons(y0, y1)))))) -> c5(MARK(length(s(length(cons(y0, y1)))))) A__LENGTH(cons(z0, length(s(length(s(y0)))))) -> c5(MARK(length(s(length(s(y0)))))) A__LENGTH(cons(z0, length(s(and(and(and(y0, y1), y2), y3))))) -> c5(MARK(length(s(and(and(and(y0, y1), y2), y3))))) A__LENGTH(cons(z0, length(s(and(and(length(y0), y1), y2))))) -> c5(MARK(length(s(and(and(length(y0), y1), y2))))) A__LENGTH(cons(z0, length(s(and(and(cons(y0, y1), y2), y3))))) -> c5(MARK(length(s(and(and(cons(y0, y1), y2), y3))))) A__LENGTH(cons(z0, length(s(and(and(tt, y0), y1))))) -> c5(MARK(length(s(and(and(tt, y0), y1))))) A__LENGTH(cons(z0, length(s(and(and(s(y0), y1), y2))))) -> c5(MARK(length(s(and(and(s(y0), y1), y2))))) A__LENGTH(cons(z0, length(s(and(and(y0, y1), y2))))) -> c5(MARK(length(s(and(and(y0, y1), y2))))) A__LENGTH(cons(z0, length(s(and(length(zeros), y0))))) -> c5(MARK(length(s(and(length(zeros), y0))))) A__LENGTH(cons(z0, length(s(and(length(and(y0, y1)), y2))))) -> c5(MARK(length(s(and(length(and(y0, y1)), y2))))) A__LENGTH(cons(z0, length(s(and(length(length(y0)), y1))))) -> c5(MARK(length(s(and(length(length(y0)), y1))))) A__LENGTH(cons(z0, length(s(and(length(cons(y0, y1)), y2))))) -> c5(MARK(length(s(and(length(cons(y0, y1)), y2))))) A__LENGTH(cons(z0, length(s(and(length(s(y0)), y1))))) -> c5(MARK(length(s(and(length(s(y0)), y1))))) A__LENGTH(cons(z0, length(s(and(length(y0), y1))))) -> c5(MARK(length(s(and(length(y0), y1))))) A__LENGTH(cons(z0, length(s(and(and(zeros, y0), y1))))) -> c5(MARK(length(s(and(and(zeros, y0), y1))))) A__LENGTH(cons(z0, length(s(length(and(and(y0, y1), y2)))))) -> c5(MARK(length(s(length(and(and(y0, y1), y2)))))) A__LENGTH(cons(z0, length(s(length(and(length(y0), y1)))))) -> c5(MARK(length(s(length(and(length(y0), y1)))))) A__LENGTH(cons(z0, length(s(length(and(cons(y0, y1), y2)))))) -> c5(MARK(length(s(length(and(cons(y0, y1), y2)))))) A__LENGTH(cons(z0, length(s(length(and(tt, y0)))))) -> c5(MARK(length(s(length(and(tt, y0)))))) A__LENGTH(cons(z0, length(s(length(and(s(y0), y1)))))) -> c5(MARK(length(s(length(and(s(y0), y1)))))) A__LENGTH(cons(z0, length(s(length(and(y0, y1)))))) -> c5(MARK(length(s(length(and(y0, y1)))))) A__LENGTH(cons(z0, length(s(length(and(zeros, y0)))))) -> c5(MARK(length(s(length(and(zeros, y0)))))) A__LENGTH(cons(z0, length(s(length(length(zeros)))))) -> c5(MARK(length(s(length(length(zeros)))))) A__LENGTH(cons(z0, length(s(length(length(and(y0, y1))))))) -> c5(MARK(length(s(length(length(and(y0, y1))))))) A__LENGTH(cons(z0, length(s(length(length(length(y0))))))) -> c5(MARK(length(s(length(length(length(y0))))))) A__LENGTH(cons(z0, length(s(length(length(cons(y0, y1))))))) -> c5(MARK(length(s(length(length(cons(y0, y1))))))) A__LENGTH(cons(z0, length(s(length(length(s(y0))))))) -> c5(MARK(length(s(length(length(s(y0))))))) A__LENGTH(cons(z0, length(s(length(length(y0)))))) -> c5(MARK(length(s(length(length(y0)))))) A__LENGTH(cons(z0, length(s(length(zeros))))) -> c5(MARK(length(s(length(zeros))))) A__LENGTH(cons(z0, length(s(cons(cons(y0, y1), y2))))) -> c5(MARK(length(s(cons(cons(y0, y1), y2))))) A__LENGTH(cons(z0, length(s(cons(s(y0), y1))))) -> c5(MARK(length(s(cons(s(y0), y1))))) A__LENGTH(cons(z0, length(s(cons(and(cons(y0, y1), y2), y3))))) -> c5(MARK(length(s(cons(and(cons(y0, y1), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(tt, y0), y1))))) -> c5(MARK(length(s(cons(and(tt, y0), y1))))) A__LENGTH(cons(z0, length(s(cons(and(s(y0), y1), y2))))) -> c5(MARK(length(s(cons(and(s(y0), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(length(cons(y0, y1)), y2))))) -> c5(MARK(length(s(cons(length(cons(y0, y1)), y2))))) A__LENGTH(cons(z0, length(s(cons(length(s(y0)), y1))))) -> c5(MARK(length(s(cons(length(s(y0)), y1))))) A__LENGTH(cons(z0, length(s(cons(and(and(and(y0, y1), y2), y3), y4))))) -> c5(MARK(length(s(cons(and(and(and(y0, y1), y2), y3), y4))))) A__LENGTH(cons(z0, length(s(cons(and(and(length(y0), y1), y2), y3))))) -> c5(MARK(length(s(cons(and(and(length(y0), y1), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(and(cons(y0, y1), y2), y3), y4))))) -> c5(MARK(length(s(cons(and(and(cons(y0, y1), y2), y3), y4))))) A__LENGTH(cons(z0, length(s(cons(and(and(tt, y0), y1), y2))))) -> c5(MARK(length(s(cons(and(and(tt, y0), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(and(and(s(y0), y1), y2), y3))))) -> c5(MARK(length(s(cons(and(and(s(y0), y1), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(and(y0, y1), y2), y3))))) -> c5(MARK(length(s(cons(and(and(y0, y1), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(length(zeros), y0), y1))))) -> c5(MARK(length(s(cons(and(length(zeros), y0), y1))))) A__LENGTH(cons(z0, length(s(cons(and(length(and(y0, y1)), y2), y3))))) -> c5(MARK(length(s(cons(and(length(and(y0, y1)), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(length(length(y0)), y1), y2))))) -> c5(MARK(length(s(cons(and(length(length(y0)), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(and(length(cons(y0, y1)), y2), y3))))) -> c5(MARK(length(s(cons(and(length(cons(y0, y1)), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(length(s(y0)), y1), y2))))) -> c5(MARK(length(s(cons(and(length(s(y0)), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(and(length(y0), y1), y2))))) -> c5(MARK(length(s(cons(and(length(y0), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(and(and(zeros, y0), y1), y2))))) -> c5(MARK(length(s(cons(and(and(zeros, y0), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(length(and(and(y0, y1), y2)), y3))))) -> c5(MARK(length(s(cons(length(and(and(y0, y1), y2)), y3))))) A__LENGTH(cons(z0, length(s(cons(length(and(length(y0), y1)), y2))))) -> c5(MARK(length(s(cons(length(and(length(y0), y1)), y2))))) A__LENGTH(cons(z0, length(s(cons(length(and(cons(y0, y1), y2)), y3))))) -> c5(MARK(length(s(cons(length(and(cons(y0, y1), y2)), y3))))) A__LENGTH(cons(z0, length(s(cons(length(and(tt, y0)), y1))))) -> c5(MARK(length(s(cons(length(and(tt, y0)), y1))))) A__LENGTH(cons(z0, length(s(cons(length(and(s(y0), y1)), y2))))) -> c5(MARK(length(s(cons(length(and(s(y0), y1)), y2))))) A__LENGTH(cons(z0, length(s(cons(length(and(y0, y1)), y2))))) -> c5(MARK(length(s(cons(length(and(y0, y1)), y2))))) A__LENGTH(cons(z0, length(s(cons(length(and(zeros, y0)), y1))))) -> c5(MARK(length(s(cons(length(and(zeros, y0)), y1))))) A__LENGTH(cons(z0, length(s(cons(length(length(zeros)), y0))))) -> c5(MARK(length(s(cons(length(length(zeros)), y0))))) A__LENGTH(cons(z0, length(s(cons(length(length(and(y0, y1))), y2))))) -> c5(MARK(length(s(cons(length(length(and(y0, y1))), y2))))) A__LENGTH(cons(z0, length(s(cons(length(length(length(y0))), y1))))) -> c5(MARK(length(s(cons(length(length(length(y0))), y1))))) A__LENGTH(cons(z0, length(s(cons(length(length(cons(y0, y1))), y2))))) -> c5(MARK(length(s(cons(length(length(cons(y0, y1))), y2))))) A__LENGTH(cons(z0, length(s(cons(length(length(s(y0))), y1))))) -> c5(MARK(length(s(cons(length(length(s(y0))), y1))))) A__LENGTH(cons(z0, length(s(cons(length(length(y0)), y1))))) -> c5(MARK(length(s(cons(length(length(y0)), y1))))) A__LENGTH(cons(z0, length(s(cons(length(zeros), y0))))) -> c5(MARK(length(s(cons(length(zeros), y0))))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__LENGTH_1, MARK_1, A__AND_2 Compound Symbols: c5_2, c9_2, c5_1, c8_2, c8_1, c9_1, c2_1, c10_1, c14_1 ---------------------------------------- (185) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(and(and(x0, z1), x2)) -> c8(MARK(and(x0, z1))) by MARK(and(and(and(and(y0, y1), y2), z1), z2)) -> c8(MARK(and(and(and(y0, y1), y2), z1))) MARK(and(and(and(length(y0), y1), z1), z2)) -> c8(MARK(and(and(length(y0), y1), z1))) MARK(and(and(and(cons(y0, y1), y2), z1), z2)) -> c8(MARK(and(and(cons(y0, y1), y2), z1))) MARK(and(and(and(tt, y0), z1), z2)) -> c8(MARK(and(and(tt, y0), z1))) MARK(and(and(and(s(y0), y1), z1), z2)) -> c8(MARK(and(and(s(y0), y1), z1))) MARK(and(and(and(y0, y1), z1), z2)) -> c8(MARK(and(and(y0, y1), z1))) MARK(and(and(length(zeros), z1), z2)) -> c8(MARK(and(length(zeros), z1))) MARK(and(and(length(and(y0, y1)), z1), z2)) -> c8(MARK(and(length(and(y0, y1)), z1))) MARK(and(and(length(length(y0)), z1), z2)) -> c8(MARK(and(length(length(y0)), z1))) MARK(and(and(length(cons(y0, y1)), z1), z2)) -> c8(MARK(and(length(cons(y0, y1)), z1))) MARK(and(and(length(s(y0)), z1), z2)) -> c8(MARK(and(length(s(y0)), z1))) MARK(and(and(length(y0), z1), z2)) -> c8(MARK(and(length(y0), z1))) MARK(and(and(and(zeros, y0), z1), z2)) -> c8(MARK(and(and(zeros, y0), z1))) MARK(and(and(cons(cons(y0, y1), y2), z1), z2)) -> c8(MARK(and(cons(cons(y0, y1), y2), z1))) MARK(and(and(cons(s(y0), y1), z1), z2)) -> c8(MARK(and(cons(s(y0), y1), z1))) MARK(and(and(cons(and(cons(y0, y1), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(cons(y0, y1), y2), y3), z1))) MARK(and(and(cons(and(tt, y0), y1), z1), z2)) -> c8(MARK(and(cons(and(tt, y0), y1), z1))) MARK(and(and(cons(and(s(y0), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(s(y0), y1), y2), z1))) MARK(and(and(cons(length(cons(y0, y1)), y2), z1), z2)) -> c8(MARK(and(cons(length(cons(y0, y1)), y2), z1))) MARK(and(and(cons(length(s(y0)), y1), z1), z2)) -> c8(MARK(and(cons(length(s(y0)), y1), z1))) MARK(and(and(cons(and(and(and(y0, y1), y2), y3), y4), z1), z2)) -> c8(MARK(and(cons(and(and(and(y0, y1), y2), y3), y4), z1))) MARK(and(and(cons(and(and(length(y0), y1), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(and(length(y0), y1), y2), y3), z1))) MARK(and(and(cons(and(and(cons(y0, y1), y2), y3), y4), z1), z2)) -> c8(MARK(and(cons(and(and(cons(y0, y1), y2), y3), y4), z1))) MARK(and(and(cons(and(and(tt, y0), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(and(tt, y0), y1), y2), z1))) MARK(and(and(cons(and(and(s(y0), y1), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(and(s(y0), y1), y2), y3), z1))) MARK(and(and(cons(and(and(y0, y1), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(and(y0, y1), y2), y3), z1))) MARK(and(and(cons(and(length(zeros), y0), y1), z1), z2)) -> c8(MARK(and(cons(and(length(zeros), y0), y1), z1))) MARK(and(and(cons(and(length(and(y0, y1)), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(length(and(y0, y1)), y2), y3), z1))) MARK(and(and(cons(and(length(length(y0)), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(length(length(y0)), y1), y2), z1))) MARK(and(and(cons(and(length(cons(y0, y1)), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(length(cons(y0, y1)), y2), y3), z1))) MARK(and(and(cons(and(length(s(y0)), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(length(s(y0)), y1), y2), z1))) MARK(and(and(cons(and(length(y0), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(length(y0), y1), y2), z1))) MARK(and(and(cons(and(and(zeros, y0), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(and(zeros, y0), y1), y2), z1))) MARK(and(and(cons(length(and(and(y0, y1), y2)), y3), z1), z2)) -> c8(MARK(and(cons(length(and(and(y0, y1), y2)), y3), z1))) MARK(and(and(cons(length(and(length(y0), y1)), y2), z1), z2)) -> c8(MARK(and(cons(length(and(length(y0), y1)), y2), z1))) MARK(and(and(cons(length(and(cons(y0, y1), y2)), y3), z1), z2)) -> c8(MARK(and(cons(length(and(cons(y0, y1), y2)), y3), z1))) MARK(and(and(cons(length(and(tt, y0)), y1), z1), z2)) -> c8(MARK(and(cons(length(and(tt, y0)), y1), z1))) MARK(and(and(cons(length(and(s(y0), y1)), y2), z1), z2)) -> c8(MARK(and(cons(length(and(s(y0), y1)), y2), z1))) MARK(and(and(cons(length(and(y0, y1)), y2), z1), z2)) -> c8(MARK(and(cons(length(and(y0, y1)), y2), z1))) MARK(and(and(cons(length(and(zeros, y0)), y1), z1), z2)) -> c8(MARK(and(cons(length(and(zeros, y0)), y1), z1))) MARK(and(and(cons(length(length(zeros)), y0), z1), z2)) -> c8(MARK(and(cons(length(length(zeros)), y0), z1))) MARK(and(and(cons(length(length(and(y0, y1))), y2), z1), z2)) -> c8(MARK(and(cons(length(length(and(y0, y1))), y2), z1))) MARK(and(and(cons(length(length(length(y0))), y1), z1), z2)) -> c8(MARK(and(cons(length(length(length(y0))), y1), z1))) MARK(and(and(cons(length(length(cons(y0, y1))), y2), z1), z2)) -> c8(MARK(and(cons(length(length(cons(y0, y1))), y2), z1))) MARK(and(and(cons(length(length(s(y0))), y1), z1), z2)) -> c8(MARK(and(cons(length(length(s(y0))), y1), z1))) MARK(and(and(cons(length(length(y0)), y1), z1), z2)) -> c8(MARK(and(cons(length(length(y0)), y1), z1))) MARK(and(and(cons(length(zeros), y0), z1), z2)) -> c8(MARK(and(cons(length(zeros), y0), z1))) MARK(and(and(tt, cons(y0, y1)), z2)) -> c8(MARK(and(tt, cons(y0, y1)))) MARK(and(and(tt, s(y0)), z2)) -> c8(MARK(and(tt, s(y0)))) MARK(and(and(tt, and(cons(y0, y1), y2)), z2)) -> c8(MARK(and(tt, and(cons(y0, y1), y2)))) MARK(and(and(tt, and(tt, y0)), z2)) -> c8(MARK(and(tt, and(tt, y0)))) MARK(and(and(tt, and(s(y0), y1)), z2)) -> c8(MARK(and(tt, and(s(y0), y1)))) MARK(and(and(tt, length(cons(y0, y1))), z2)) -> c8(MARK(and(tt, length(cons(y0, y1))))) MARK(and(and(tt, length(s(y0))), z2)) -> c8(MARK(and(tt, length(s(y0))))) MARK(and(and(tt, and(and(and(y0, y1), y2), y3)), z2)) -> c8(MARK(and(tt, and(and(and(y0, y1), y2), y3)))) MARK(and(and(tt, and(and(length(y0), y1), y2)), z2)) -> c8(MARK(and(tt, and(and(length(y0), y1), y2)))) MARK(and(and(tt, and(and(cons(y0, y1), y2), y3)), z2)) -> c8(MARK(and(tt, and(and(cons(y0, y1), y2), y3)))) MARK(and(and(tt, and(and(tt, y0), y1)), z2)) -> c8(MARK(and(tt, and(and(tt, y0), y1)))) MARK(and(and(tt, and(and(s(y0), y1), y2)), z2)) -> c8(MARK(and(tt, and(and(s(y0), y1), y2)))) MARK(and(and(tt, and(and(y0, y1), y2)), z2)) -> c8(MARK(and(tt, and(and(y0, y1), y2)))) MARK(and(and(tt, and(length(zeros), y0)), z2)) -> c8(MARK(and(tt, and(length(zeros), y0)))) MARK(and(and(tt, and(length(and(y0, y1)), y2)), z2)) -> c8(MARK(and(tt, and(length(and(y0, y1)), y2)))) MARK(and(and(tt, and(length(length(y0)), y1)), z2)) -> c8(MARK(and(tt, and(length(length(y0)), y1)))) MARK(and(and(tt, and(length(cons(y0, y1)), y2)), z2)) -> c8(MARK(and(tt, and(length(cons(y0, y1)), y2)))) MARK(and(and(tt, and(length(s(y0)), y1)), z2)) -> c8(MARK(and(tt, and(length(s(y0)), y1)))) MARK(and(and(tt, and(length(y0), y1)), z2)) -> c8(MARK(and(tt, and(length(y0), y1)))) MARK(and(and(tt, and(and(zeros, y0), y1)), z2)) -> c8(MARK(and(tt, and(and(zeros, y0), y1)))) MARK(and(and(tt, length(and(and(y0, y1), y2))), z2)) -> c8(MARK(and(tt, length(and(and(y0, y1), y2))))) MARK(and(and(tt, length(and(length(y0), y1))), z2)) -> c8(MARK(and(tt, length(and(length(y0), y1))))) MARK(and(and(tt, length(and(cons(y0, y1), y2))), z2)) -> c8(MARK(and(tt, length(and(cons(y0, y1), y2))))) MARK(and(and(tt, length(and(tt, y0))), z2)) -> c8(MARK(and(tt, length(and(tt, y0))))) MARK(and(and(tt, length(and(s(y0), y1))), z2)) -> c8(MARK(and(tt, length(and(s(y0), y1))))) MARK(and(and(tt, length(and(y0, y1))), z2)) -> c8(MARK(and(tt, length(and(y0, y1))))) MARK(and(and(tt, length(and(zeros, y0))), z2)) -> c8(MARK(and(tt, length(and(zeros, y0))))) MARK(and(and(tt, length(length(zeros))), z2)) -> c8(MARK(and(tt, length(length(zeros))))) MARK(and(and(tt, length(length(and(y0, y1)))), z2)) -> c8(MARK(and(tt, length(length(and(y0, y1)))))) MARK(and(and(tt, length(length(length(y0)))), z2)) -> c8(MARK(and(tt, length(length(length(y0)))))) MARK(and(and(tt, length(length(cons(y0, y1)))), z2)) -> c8(MARK(and(tt, length(length(cons(y0, y1)))))) MARK(and(and(tt, length(length(s(y0)))), z2)) -> c8(MARK(and(tt, length(length(s(y0)))))) MARK(and(and(tt, length(length(y0))), z2)) -> c8(MARK(and(tt, length(length(y0))))) MARK(and(and(tt, length(zeros)), z2)) -> c8(MARK(and(tt, length(zeros)))) MARK(and(and(s(s(y0)), z1), z2)) -> c8(MARK(and(s(s(y0)), z1))) MARK(and(and(s(and(cons(y0, y1), y2)), z1), z2)) -> c8(MARK(and(s(and(cons(y0, y1), y2)), z1))) MARK(and(and(s(and(tt, y0)), z1), z2)) -> c8(MARK(and(s(and(tt, y0)), z1))) MARK(and(and(s(and(s(y0), y1)), z1), z2)) -> c8(MARK(and(s(and(s(y0), y1)), z1))) MARK(and(and(s(length(cons(y0, y1))), z1), z2)) -> c8(MARK(and(s(length(cons(y0, y1))), z1))) MARK(and(and(s(length(s(y0))), z1), z2)) -> c8(MARK(and(s(length(s(y0))), z1))) MARK(and(and(s(and(and(and(y0, y1), y2), y3)), z1), z2)) -> c8(MARK(and(s(and(and(and(y0, y1), y2), y3)), z1))) MARK(and(and(s(and(and(length(y0), y1), y2)), z1), z2)) -> c8(MARK(and(s(and(and(length(y0), y1), y2)), z1))) MARK(and(and(s(and(and(cons(y0, y1), y2), y3)), z1), z2)) -> c8(MARK(and(s(and(and(cons(y0, y1), y2), y3)), z1))) MARK(and(and(s(and(and(tt, y0), y1)), z1), z2)) -> c8(MARK(and(s(and(and(tt, y0), y1)), z1))) MARK(and(and(s(and(and(s(y0), y1), y2)), z1), z2)) -> c8(MARK(and(s(and(and(s(y0), y1), y2)), z1))) MARK(and(and(s(and(and(y0, y1), y2)), z1), z2)) -> c8(MARK(and(s(and(and(y0, y1), y2)), z1))) MARK(and(and(s(and(length(zeros), y0)), z1), z2)) -> c8(MARK(and(s(and(length(zeros), y0)), z1))) MARK(and(and(s(and(length(and(y0, y1)), y2)), z1), z2)) -> c8(MARK(and(s(and(length(and(y0, y1)), y2)), z1))) MARK(and(and(s(and(length(length(y0)), y1)), z1), z2)) -> c8(MARK(and(s(and(length(length(y0)), y1)), z1))) MARK(and(and(s(and(length(cons(y0, y1)), y2)), z1), z2)) -> c8(MARK(and(s(and(length(cons(y0, y1)), y2)), z1))) MARK(and(and(s(and(length(s(y0)), y1)), z1), z2)) -> c8(MARK(and(s(and(length(s(y0)), y1)), z1))) MARK(and(and(s(and(length(y0), y1)), z1), z2)) -> c8(MARK(and(s(and(length(y0), y1)), z1))) MARK(and(and(s(and(and(zeros, y0), y1)), z1), z2)) -> c8(MARK(and(s(and(and(zeros, y0), y1)), z1))) MARK(and(and(s(length(and(and(y0, y1), y2))), z1), z2)) -> c8(MARK(and(s(length(and(and(y0, y1), y2))), z1))) MARK(and(and(s(length(and(length(y0), y1))), z1), z2)) -> c8(MARK(and(s(length(and(length(y0), y1))), z1))) MARK(and(and(s(length(and(cons(y0, y1), y2))), z1), z2)) -> c8(MARK(and(s(length(and(cons(y0, y1), y2))), z1))) MARK(and(and(s(length(and(tt, y0))), z1), z2)) -> c8(MARK(and(s(length(and(tt, y0))), z1))) MARK(and(and(s(length(and(s(y0), y1))), z1), z2)) -> c8(MARK(and(s(length(and(s(y0), y1))), z1))) MARK(and(and(s(length(and(y0, y1))), z1), z2)) -> c8(MARK(and(s(length(and(y0, y1))), z1))) MARK(and(and(s(length(and(zeros, y0))), z1), z2)) -> c8(MARK(and(s(length(and(zeros, y0))), z1))) MARK(and(and(s(length(length(zeros))), z1), z2)) -> c8(MARK(and(s(length(length(zeros))), z1))) MARK(and(and(s(length(length(and(y0, y1)))), z1), z2)) -> c8(MARK(and(s(length(length(and(y0, y1)))), z1))) MARK(and(and(s(length(length(length(y0)))), z1), z2)) -> c8(MARK(and(s(length(length(length(y0)))), z1))) MARK(and(and(s(length(length(cons(y0, y1)))), z1), z2)) -> c8(MARK(and(s(length(length(cons(y0, y1)))), z1))) MARK(and(and(s(length(length(s(y0)))), z1), z2)) -> c8(MARK(and(s(length(length(s(y0)))), z1))) MARK(and(and(s(length(length(y0))), z1), z2)) -> c8(MARK(and(s(length(length(y0))), z1))) MARK(and(and(s(length(zeros)), z1), z2)) -> c8(MARK(and(s(length(zeros)), z1))) MARK(and(and(s(cons(cons(y0, y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(cons(y0, y1), y2)), z1))) MARK(and(and(s(cons(s(y0), y1)), z1), z2)) -> c8(MARK(and(s(cons(s(y0), y1)), z1))) MARK(and(and(s(cons(and(cons(y0, y1), y2), y3)), z1), z2)) -> c8(MARK(and(s(cons(and(cons(y0, y1), y2), y3)), z1))) MARK(and(and(s(cons(and(tt, y0), y1)), z1), z2)) -> c8(MARK(and(s(cons(and(tt, y0), y1)), z1))) MARK(and(and(s(cons(and(s(y0), y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(and(s(y0), y1), y2)), z1))) MARK(and(and(s(cons(length(cons(y0, y1)), y2)), z1), z2)) -> c8(MARK(and(s(cons(length(cons(y0, y1)), y2)), z1))) MARK(and(and(s(cons(length(s(y0)), y1)), z1), z2)) -> c8(MARK(and(s(cons(length(s(y0)), y1)), z1))) MARK(and(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), z1), z2)) -> c8(MARK(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), z1))) MARK(and(and(s(cons(and(and(length(y0), y1), y2), y3)), z1), z2)) -> c8(MARK(and(s(cons(and(and(length(y0), y1), y2), y3)), z1))) MARK(and(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), z1), z2)) -> c8(MARK(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), z1))) MARK(and(and(s(cons(and(and(tt, y0), y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(and(and(tt, y0), y1), y2)), z1))) MARK(and(and(s(cons(and(and(s(y0), y1), y2), y3)), z1), z2)) -> c8(MARK(and(s(cons(and(and(s(y0), y1), y2), y3)), z1))) MARK(and(and(s(cons(and(and(y0, y1), y2), y3)), z1), z2)) -> c8(MARK(and(s(cons(and(and(y0, y1), y2), y3)), z1))) MARK(and(and(s(cons(and(length(zeros), y0), y1)), z1), z2)) -> c8(MARK(and(s(cons(and(length(zeros), y0), y1)), z1))) MARK(and(and(s(cons(and(length(and(y0, y1)), y2), y3)), z1), z2)) -> c8(MARK(and(s(cons(and(length(and(y0, y1)), y2), y3)), z1))) MARK(and(and(s(cons(and(length(length(y0)), y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(and(length(length(y0)), y1), y2)), z1))) MARK(and(and(s(cons(and(length(cons(y0, y1)), y2), y3)), z1), z2)) -> c8(MARK(and(s(cons(and(length(cons(y0, y1)), y2), y3)), z1))) MARK(and(and(s(cons(and(length(s(y0)), y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(and(length(s(y0)), y1), y2)), z1))) MARK(and(and(s(cons(and(length(y0), y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(and(length(y0), y1), y2)), z1))) MARK(and(and(s(cons(and(and(zeros, y0), y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(and(and(zeros, y0), y1), y2)), z1))) MARK(and(and(s(cons(length(and(and(y0, y1), y2)), y3)), z1), z2)) -> c8(MARK(and(s(cons(length(and(and(y0, y1), y2)), y3)), z1))) MARK(and(and(s(cons(length(and(length(y0), y1)), y2)), z1), z2)) -> c8(MARK(and(s(cons(length(and(length(y0), y1)), y2)), z1))) MARK(and(and(s(cons(length(and(cons(y0, y1), y2)), y3)), z1), z2)) -> c8(MARK(and(s(cons(length(and(cons(y0, y1), y2)), y3)), z1))) MARK(and(and(s(cons(length(and(tt, y0)), y1)), z1), z2)) -> c8(MARK(and(s(cons(length(and(tt, y0)), y1)), z1))) MARK(and(and(s(cons(length(and(s(y0), y1)), y2)), z1), z2)) -> c8(MARK(and(s(cons(length(and(s(y0), y1)), y2)), z1))) MARK(and(and(s(cons(length(and(y0, y1)), y2)), z1), z2)) -> c8(MARK(and(s(cons(length(and(y0, y1)), y2)), z1))) MARK(and(and(s(cons(length(and(zeros, y0)), y1)), z1), z2)) -> c8(MARK(and(s(cons(length(and(zeros, y0)), y1)), z1))) MARK(and(and(s(cons(length(length(zeros)), y0)), z1), z2)) -> c8(MARK(and(s(cons(length(length(zeros)), y0)), z1))) MARK(and(and(s(cons(length(length(and(y0, y1))), y2)), z1), z2)) -> c8(MARK(and(s(cons(length(length(and(y0, y1))), y2)), z1))) MARK(and(and(s(cons(length(length(length(y0))), y1)), z1), z2)) -> c8(MARK(and(s(cons(length(length(length(y0))), y1)), z1))) MARK(and(and(s(cons(length(length(cons(y0, y1))), y2)), z1), z2)) -> c8(MARK(and(s(cons(length(length(cons(y0, y1))), y2)), z1))) MARK(and(and(s(cons(length(length(s(y0))), y1)), z1), z2)) -> c8(MARK(and(s(cons(length(length(s(y0))), y1)), z1))) MARK(and(and(s(cons(length(length(y0)), y1)), z1), z2)) -> c8(MARK(and(s(cons(length(length(y0)), y1)), z1))) MARK(and(and(s(cons(length(zeros), y0)), z1), z2)) -> c8(MARK(and(s(cons(length(zeros), y0)), z1))) ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) MARK(cons(and(and(cons(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(cons(y0, y1), y2), y3))) MARK(cons(and(and(tt, y0), y1), z1)) -> c10(MARK(and(and(tt, y0), y1))) MARK(cons(and(and(s(y0), y1), y2), z1)) -> c10(MARK(and(and(s(y0), y1), y2))) MARK(cons(and(and(y0, y1), y2), z1)) -> c10(MARK(and(and(y0, y1), y2))) MARK(cons(and(length(zeros), y0), z1)) -> c10(MARK(and(length(zeros), y0))) MARK(cons(and(length(and(y0, y1)), y2), z1)) -> c10(MARK(and(length(and(y0, y1)), y2))) MARK(cons(and(length(length(y0)), y1), z1)) -> c10(MARK(and(length(length(y0)), y1))) MARK(cons(and(length(cons(y0, y1)), y2), z1)) -> c10(MARK(and(length(cons(y0, y1)), y2))) MARK(cons(and(length(s(y0)), y1), z1)) -> c10(MARK(and(length(s(y0)), y1))) MARK(cons(and(length(y0), y1), z1)) -> c10(MARK(and(length(y0), y1))) MARK(cons(and(and(zeros, y0), y1), z1)) -> c10(MARK(and(and(zeros, y0), y1))) MARK(cons(length(and(and(y0, y1), y2)), z1)) -> c10(MARK(length(and(and(y0, y1), y2)))) MARK(cons(length(and(length(y0), y1)), z1)) -> c10(MARK(length(and(length(y0), y1)))) MARK(cons(length(and(cons(y0, y1), y2)), z1)) -> c10(MARK(length(and(cons(y0, y1), y2)))) MARK(cons(length(and(tt, y0)), z1)) -> c10(MARK(length(and(tt, y0)))) MARK(cons(length(and(s(y0), y1)), z1)) -> c10(MARK(length(and(s(y0), y1)))) MARK(cons(length(and(y0, y1)), z1)) -> c10(MARK(length(and(y0, y1)))) MARK(cons(length(and(zeros, y0)), z1)) -> c10(MARK(length(and(zeros, y0)))) MARK(cons(length(length(zeros)), z1)) -> c10(MARK(length(length(zeros)))) MARK(cons(length(length(and(y0, y1))), z1)) -> c10(MARK(length(length(and(y0, y1))))) MARK(cons(length(length(length(y0))), z1)) -> c10(MARK(length(length(length(y0))))) MARK(cons(length(length(cons(y0, y1))), z1)) -> c10(MARK(length(length(cons(y0, y1))))) MARK(cons(length(length(s(y0))), z1)) -> c10(MARK(length(length(s(y0))))) MARK(cons(length(length(y0)), z1)) -> c10(MARK(length(length(y0)))) MARK(cons(length(zeros), z1)) -> c10(MARK(length(zeros))) MARK(s(s(y0))) -> c14(MARK(s(y0))) MARK(s(and(cons(y0, y1), y2))) -> c14(MARK(and(cons(y0, y1), y2))) MARK(s(and(tt, y0))) -> c14(MARK(and(tt, y0))) MARK(s(and(s(y0), y1))) -> c14(MARK(and(s(y0), y1))) MARK(s(length(cons(y0, y1)))) -> c14(MARK(length(cons(y0, y1)))) MARK(s(length(s(y0)))) -> c14(MARK(length(s(y0)))) MARK(s(and(and(and(y0, y1), y2), y3))) -> c14(MARK(and(and(and(y0, y1), y2), y3))) MARK(s(and(and(length(y0), y1), y2))) -> c14(MARK(and(and(length(y0), y1), y2))) MARK(s(and(and(cons(y0, y1), y2), y3))) -> c14(MARK(and(and(cons(y0, y1), y2), y3))) MARK(s(and(and(tt, y0), y1))) -> c14(MARK(and(and(tt, y0), y1))) MARK(s(and(and(s(y0), y1), y2))) -> c14(MARK(and(and(s(y0), y1), y2))) MARK(s(and(and(y0, y1), y2))) -> c14(MARK(and(and(y0, y1), y2))) MARK(s(and(length(zeros), y0))) -> c14(MARK(and(length(zeros), y0))) MARK(s(and(length(and(y0, y1)), y2))) -> c14(MARK(and(length(and(y0, y1)), y2))) MARK(s(and(length(length(y0)), y1))) -> c14(MARK(and(length(length(y0)), y1))) MARK(s(and(length(cons(y0, y1)), y2))) -> c14(MARK(and(length(cons(y0, y1)), y2))) MARK(s(and(length(s(y0)), y1))) -> c14(MARK(and(length(s(y0)), y1))) MARK(s(and(length(y0), y1))) -> c14(MARK(and(length(y0), y1))) MARK(s(and(and(zeros, y0), y1))) -> c14(MARK(and(and(zeros, y0), y1))) MARK(s(length(and(and(y0, y1), y2)))) -> c14(MARK(length(and(and(y0, y1), y2)))) MARK(s(length(and(length(y0), y1)))) -> c14(MARK(length(and(length(y0), y1)))) MARK(s(length(and(cons(y0, y1), y2)))) -> c14(MARK(length(and(cons(y0, y1), y2)))) MARK(s(length(and(tt, y0)))) -> c14(MARK(length(and(tt, y0)))) MARK(s(length(and(s(y0), y1)))) -> c14(MARK(length(and(s(y0), y1)))) MARK(s(length(and(y0, y1)))) -> c14(MARK(length(and(y0, y1)))) MARK(s(length(and(zeros, y0)))) -> c14(MARK(length(and(zeros, y0)))) MARK(s(length(length(zeros)))) -> c14(MARK(length(length(zeros)))) MARK(s(length(length(and(y0, y1))))) -> c14(MARK(length(length(and(y0, y1))))) MARK(s(length(length(length(y0))))) -> c14(MARK(length(length(length(y0))))) MARK(s(length(length(cons(y0, y1))))) -> c14(MARK(length(length(cons(y0, y1))))) MARK(s(length(length(s(y0))))) -> c14(MARK(length(length(s(y0))))) MARK(s(length(length(y0)))) -> c14(MARK(length(length(y0)))) MARK(s(length(zeros))) -> c14(MARK(length(zeros))) MARK(s(cons(cons(y0, y1), y2))) -> c14(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c14(MARK(cons(s(y0), y1))) MARK(s(cons(and(cons(y0, y1), y2), y3))) -> c14(MARK(cons(and(cons(y0, y1), y2), y3))) MARK(s(cons(and(tt, y0), y1))) -> c14(MARK(cons(and(tt, y0), y1))) MARK(s(cons(and(s(y0), y1), y2))) -> c14(MARK(cons(and(s(y0), y1), y2))) MARK(s(cons(length(cons(y0, y1)), y2))) -> c14(MARK(cons(length(cons(y0, y1)), y2))) MARK(s(cons(length(s(y0)), y1))) -> c14(MARK(cons(length(s(y0)), y1))) MARK(s(cons(and(and(and(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(and(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(length(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(length(y0), y1), y2), y3))) MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(cons(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(tt, y0), y1), y2))) -> c14(MARK(cons(and(and(tt, y0), y1), y2))) MARK(s(cons(and(and(s(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(s(y0), y1), y2), y3))) MARK(s(cons(and(and(y0, y1), y2), y3))) -> c14(MARK(cons(and(and(y0, y1), y2), y3))) MARK(s(cons(and(length(zeros), y0), y1))) -> c14(MARK(cons(and(length(zeros), y0), y1))) MARK(s(cons(and(length(and(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(and(y0, y1)), y2), y3))) MARK(s(cons(and(length(length(y0)), y1), y2))) -> c14(MARK(cons(and(length(length(y0)), y1), y2))) MARK(s(cons(and(length(cons(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(cons(y0, y1)), y2), y3))) MARK(s(cons(and(length(s(y0)), y1), y2))) -> c14(MARK(cons(and(length(s(y0)), y1), y2))) MARK(s(cons(and(length(y0), y1), y2))) -> c14(MARK(cons(and(length(y0), y1), y2))) MARK(s(cons(and(and(zeros, y0), y1), y2))) -> c14(MARK(cons(and(and(zeros, y0), y1), y2))) MARK(s(cons(length(and(and(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(and(y0, y1), y2)), y3))) MARK(s(cons(length(and(length(y0), y1)), y2))) -> c14(MARK(cons(length(and(length(y0), y1)), y2))) MARK(s(cons(length(and(cons(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(cons(y0, y1), y2)), y3))) MARK(s(cons(length(and(tt, y0)), y1))) -> c14(MARK(cons(length(and(tt, y0)), y1))) MARK(s(cons(length(and(s(y0), y1)), y2))) -> c14(MARK(cons(length(and(s(y0), y1)), y2))) MARK(s(cons(length(and(y0, y1)), y2))) -> c14(MARK(cons(length(and(y0, y1)), y2))) MARK(s(cons(length(and(zeros, y0)), y1))) -> c14(MARK(cons(length(and(zeros, y0)), y1))) MARK(s(cons(length(length(zeros)), y0))) -> c14(MARK(cons(length(length(zeros)), y0))) MARK(s(cons(length(length(and(y0, y1))), y2))) -> c14(MARK(cons(length(length(and(y0, y1))), y2))) MARK(s(cons(length(length(length(y0))), y1))) -> c14(MARK(cons(length(length(length(y0))), y1))) MARK(s(cons(length(length(cons(y0, y1))), y2))) -> c14(MARK(cons(length(length(cons(y0, y1))), y2))) MARK(s(cons(length(length(s(y0))), y1))) -> c14(MARK(cons(length(length(s(y0))), y1))) MARK(s(cons(length(length(y0)), y1))) -> c14(MARK(cons(length(length(y0)), y1))) MARK(s(cons(length(zeros), y0))) -> c14(MARK(cons(length(zeros), y0))) A__LENGTH(cons(z0, s(s(y0)))) -> c5(MARK(s(s(y0)))) A__LENGTH(cons(z0, s(and(cons(y0, y1), y2)))) -> c5(MARK(s(and(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(tt, y0)))) -> c5(MARK(s(and(tt, y0)))) A__LENGTH(cons(z0, s(and(s(y0), y1)))) -> c5(MARK(s(and(s(y0), y1)))) A__LENGTH(cons(z0, s(length(cons(y0, y1))))) -> c5(MARK(s(length(cons(y0, y1))))) A__LENGTH(cons(z0, s(length(s(y0))))) -> c5(MARK(s(length(s(y0))))) A__LENGTH(cons(z0, s(and(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(length(y0), y1), y2)))) -> c5(MARK(s(and(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(tt, y0), y1)))) -> c5(MARK(s(and(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(and(and(s(y0), y1), y2)))) -> c5(MARK(s(and(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(y0, y1), y2)))) -> c5(MARK(s(and(and(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(length(zeros), y0)))) -> c5(MARK(s(and(length(zeros), y0)))) A__LENGTH(cons(z0, s(and(length(and(y0, y1)), y2)))) -> c5(MARK(s(and(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(length(y0)), y1)))) -> c5(MARK(s(and(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(cons(y0, y1)), y2)))) -> c5(MARK(s(and(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(s(y0)), y1)))) -> c5(MARK(s(and(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(y0), y1)))) -> c5(MARK(s(and(length(y0), y1)))) A__LENGTH(cons(z0, s(and(and(zeros, y0), y1)))) -> c5(MARK(s(and(and(zeros, y0), y1)))) A__LENGTH(cons(z0, s(length(and(and(y0, y1), y2))))) -> c5(MARK(s(length(and(and(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(length(y0), y1))))) -> c5(MARK(s(length(and(length(y0), y1))))) A__LENGTH(cons(z0, s(length(and(cons(y0, y1), y2))))) -> c5(MARK(s(length(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(tt, y0))))) -> c5(MARK(s(length(and(tt, y0))))) A__LENGTH(cons(z0, s(length(and(s(y0), y1))))) -> c5(MARK(s(length(and(s(y0), y1))))) A__LENGTH(cons(z0, s(length(and(y0, y1))))) -> c5(MARK(s(length(and(y0, y1))))) A__LENGTH(cons(z0, s(length(and(zeros, y0))))) -> c5(MARK(s(length(and(zeros, y0))))) A__LENGTH(cons(z0, s(length(length(zeros))))) -> c5(MARK(s(length(length(zeros))))) A__LENGTH(cons(z0, s(length(length(and(y0, y1)))))) -> c5(MARK(s(length(length(and(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(length(y0)))))) -> c5(MARK(s(length(length(length(y0)))))) A__LENGTH(cons(z0, s(length(length(cons(y0, y1)))))) -> c5(MARK(s(length(length(cons(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(s(y0)))))) -> 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c5(MARK(and(tt, length(length(s(y0)))))) A__LENGTH(cons(z0, and(tt, length(length(y0))))) -> c5(MARK(and(tt, length(length(y0))))) A__LENGTH(cons(z0, and(tt, length(zeros)))) -> c5(MARK(and(tt, length(zeros)))) A__LENGTH(cons(z0, and(s(s(y0)), z2))) -> c5(MARK(and(s(s(y0)), z2))) A__LENGTH(cons(z0, and(s(and(cons(y0, y1), y2)), z2))) -> c5(MARK(and(s(and(cons(y0, y1), y2)), z2))) A__LENGTH(cons(z0, and(s(and(tt, y0)), z2))) -> c5(MARK(and(s(and(tt, y0)), z2))) A__LENGTH(cons(z0, and(s(and(s(y0), y1)), z2))) -> c5(MARK(and(s(and(s(y0), y1)), z2))) A__LENGTH(cons(z0, and(s(length(cons(y0, y1))), z2))) -> c5(MARK(and(s(length(cons(y0, y1))), z2))) A__LENGTH(cons(z0, and(s(length(s(y0))), z2))) -> c5(MARK(and(s(length(s(y0))), z2))) A__LENGTH(cons(z0, and(s(and(and(and(y0, y1), y2), y3)), z2))) -> c5(MARK(and(s(and(and(and(y0, y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(and(and(length(y0), y1), y2)), z2))) -> c5(MARK(and(s(and(and(length(y0), y1), y2)), z2))) A__LENGTH(cons(z0, 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c5(MARK(and(s(length(length(zeros))), z2))) A__LENGTH(cons(z0, and(s(length(length(and(y0, y1)))), z2))) -> c5(MARK(and(s(length(length(and(y0, y1)))), z2))) A__LENGTH(cons(z0, and(s(length(length(length(y0)))), z2))) -> c5(MARK(and(s(length(length(length(y0)))), z2))) A__LENGTH(cons(z0, and(s(length(length(cons(y0, y1)))), z2))) -> c5(MARK(and(s(length(length(cons(y0, y1)))), z2))) A__LENGTH(cons(z0, and(s(length(length(s(y0)))), z2))) -> c5(MARK(and(s(length(length(s(y0)))), z2))) A__LENGTH(cons(z0, and(s(length(length(y0))), z2))) -> c5(MARK(and(s(length(length(y0))), z2))) A__LENGTH(cons(z0, and(s(length(zeros)), z2))) -> c5(MARK(and(s(length(zeros)), z2))) A__LENGTH(cons(z0, and(s(cons(cons(y0, y1), y2)), z2))) -> c5(MARK(and(s(cons(cons(y0, y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(s(y0), y1)), z2))) -> c5(MARK(and(s(cons(s(y0), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(and(cons(y0, y1), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(cons(y0, y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(tt, y0), y1)), z2))) -> c5(MARK(and(s(cons(and(tt, y0), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(and(s(y0), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(s(y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(cons(y0, y1)), y2)), z2))) -> c5(MARK(and(s(cons(length(cons(y0, y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(s(y0)), y1)), z2))) -> c5(MARK(and(s(cons(length(s(y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(and(y0, y1), y2), y3), y4)), z2))) -> c5(MARK(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(length(y0), y1), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(and(length(y0), y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), z2))) -> c5(MARK(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(tt, y0), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(and(tt, y0), y1), y2)), z2))) A__LENGTH(cons(z0, 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A__LENGTH(cons(z0, and(s(cons(and(and(zeros, y0), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(and(zeros, y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(and(y0, y1), y2)), y3)), z2))) -> c5(MARK(and(s(cons(length(and(and(y0, y1), y2)), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(length(y0), y1)), y2)), z2))) -> c5(MARK(and(s(cons(length(and(length(y0), y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(cons(y0, y1), y2)), y3)), z2))) -> c5(MARK(and(s(cons(length(and(cons(y0, y1), y2)), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(tt, y0)), y1)), z2))) -> c5(MARK(and(s(cons(length(and(tt, y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(s(y0), y1)), y2)), z2))) -> c5(MARK(and(s(cons(length(and(s(y0), y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(y0, y1)), y2)), z2))) -> c5(MARK(and(s(cons(length(and(y0, y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(zeros, y0)), y1)), z2))) -> c5(MARK(and(s(cons(length(and(zeros, 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y3))))) -> c5(MARK(length(s(cons(length(and(and(y0, y1), y2)), y3))))) A__LENGTH(cons(z0, length(s(cons(length(and(length(y0), y1)), y2))))) -> c5(MARK(length(s(cons(length(and(length(y0), y1)), y2))))) A__LENGTH(cons(z0, length(s(cons(length(and(cons(y0, y1), y2)), y3))))) -> c5(MARK(length(s(cons(length(and(cons(y0, y1), y2)), y3))))) A__LENGTH(cons(z0, length(s(cons(length(and(tt, y0)), y1))))) -> c5(MARK(length(s(cons(length(and(tt, y0)), y1))))) A__LENGTH(cons(z0, length(s(cons(length(and(s(y0), y1)), y2))))) -> c5(MARK(length(s(cons(length(and(s(y0), y1)), y2))))) A__LENGTH(cons(z0, length(s(cons(length(and(y0, y1)), y2))))) -> c5(MARK(length(s(cons(length(and(y0, y1)), y2))))) A__LENGTH(cons(z0, length(s(cons(length(and(zeros, y0)), y1))))) -> c5(MARK(length(s(cons(length(and(zeros, y0)), y1))))) A__LENGTH(cons(z0, length(s(cons(length(length(zeros)), y0))))) -> c5(MARK(length(s(cons(length(length(zeros)), y0))))) A__LENGTH(cons(z0, length(s(cons(length(length(and(y0, y1))), y2))))) -> c5(MARK(length(s(cons(length(length(and(y0, y1))), y2))))) A__LENGTH(cons(z0, length(s(cons(length(length(length(y0))), y1))))) -> c5(MARK(length(s(cons(length(length(length(y0))), y1))))) A__LENGTH(cons(z0, length(s(cons(length(length(cons(y0, y1))), y2))))) -> c5(MARK(length(s(cons(length(length(cons(y0, y1))), y2))))) A__LENGTH(cons(z0, length(s(cons(length(length(s(y0))), y1))))) -> c5(MARK(length(s(cons(length(length(s(y0))), y1))))) A__LENGTH(cons(z0, length(s(cons(length(length(y0)), y1))))) -> c5(MARK(length(s(cons(length(length(y0)), y1))))) A__LENGTH(cons(z0, length(s(cons(length(zeros), y0))))) -> c5(MARK(length(s(cons(length(zeros), y0))))) MARK(and(and(and(and(y0, y1), y2), z1), z2)) -> c8(MARK(and(and(and(y0, y1), y2), z1))) MARK(and(and(and(length(y0), y1), z1), z2)) -> c8(MARK(and(and(length(y0), y1), z1))) MARK(and(and(and(cons(y0, y1), y2), z1), z2)) -> c8(MARK(and(and(cons(y0, y1), y2), z1))) MARK(and(and(and(tt, y0), z1), z2)) -> c8(MARK(and(and(tt, y0), 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MARK(and(and(cons(length(length(length(y0))), y1), z1), z2)) -> c8(MARK(and(cons(length(length(length(y0))), y1), z1))) MARK(and(and(cons(length(length(cons(y0, y1))), y2), z1), z2)) -> c8(MARK(and(cons(length(length(cons(y0, y1))), y2), z1))) MARK(and(and(cons(length(length(s(y0))), y1), z1), z2)) -> c8(MARK(and(cons(length(length(s(y0))), y1), z1))) MARK(and(and(cons(length(length(y0)), y1), z1), z2)) -> c8(MARK(and(cons(length(length(y0)), y1), z1))) MARK(and(and(cons(length(zeros), y0), z1), z2)) -> c8(MARK(and(cons(length(zeros), y0), z1))) MARK(and(and(tt, cons(y0, y1)), z2)) -> c8(MARK(and(tt, cons(y0, y1)))) MARK(and(and(tt, s(y0)), z2)) -> c8(MARK(and(tt, s(y0)))) MARK(and(and(tt, and(cons(y0, y1), y2)), z2)) -> c8(MARK(and(tt, and(cons(y0, y1), y2)))) MARK(and(and(tt, and(tt, y0)), z2)) -> c8(MARK(and(tt, and(tt, y0)))) MARK(and(and(tt, and(s(y0), y1)), z2)) -> c8(MARK(and(tt, and(s(y0), y1)))) MARK(and(and(tt, length(cons(y0, y1))), z2)) -> c8(MARK(and(tt, length(cons(y0, 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c8(MARK(and(s(cons(cons(y0, y1), y2)), z1))) MARK(and(and(s(cons(s(y0), y1)), z1), z2)) -> c8(MARK(and(s(cons(s(y0), y1)), z1))) MARK(and(and(s(cons(and(cons(y0, y1), y2), y3)), z1), z2)) -> c8(MARK(and(s(cons(and(cons(y0, y1), y2), y3)), z1))) MARK(and(and(s(cons(and(tt, y0), y1)), z1), z2)) -> c8(MARK(and(s(cons(and(tt, y0), y1)), z1))) MARK(and(and(s(cons(and(s(y0), y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(and(s(y0), y1), y2)), z1))) MARK(and(and(s(cons(length(cons(y0, y1)), y2)), z1), z2)) -> c8(MARK(and(s(cons(length(cons(y0, y1)), y2)), z1))) MARK(and(and(s(cons(length(s(y0)), y1)), z1), z2)) -> c8(MARK(and(s(cons(length(s(y0)), y1)), z1))) MARK(and(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), z1), z2)) -> c8(MARK(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), z1))) MARK(and(and(s(cons(and(and(length(y0), y1), y2), y3)), z1), z2)) -> c8(MARK(and(s(cons(and(and(length(y0), y1), y2), y3)), z1))) MARK(and(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), z1), z2)) -> c8(MARK(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), z1))) MARK(and(and(s(cons(and(and(tt, y0), y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(and(and(tt, y0), y1), y2)), z1))) MARK(and(and(s(cons(and(and(s(y0), y1), y2), y3)), z1), z2)) -> c8(MARK(and(s(cons(and(and(s(y0), y1), y2), y3)), z1))) MARK(and(and(s(cons(and(and(y0, y1), y2), y3)), z1), z2)) -> c8(MARK(and(s(cons(and(and(y0, y1), y2), y3)), z1))) MARK(and(and(s(cons(and(length(zeros), y0), y1)), z1), z2)) -> c8(MARK(and(s(cons(and(length(zeros), y0), y1)), z1))) MARK(and(and(s(cons(and(length(and(y0, y1)), y2), y3)), z1), z2)) -> c8(MARK(and(s(cons(and(length(and(y0, y1)), y2), y3)), z1))) MARK(and(and(s(cons(and(length(length(y0)), y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(and(length(length(y0)), y1), y2)), z1))) MARK(and(and(s(cons(and(length(cons(y0, y1)), y2), y3)), z1), z2)) -> c8(MARK(and(s(cons(and(length(cons(y0, y1)), y2), y3)), z1))) MARK(and(and(s(cons(and(length(s(y0)), y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(and(length(s(y0)), y1), y2)), z1))) MARK(and(and(s(cons(and(length(y0), y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(and(length(y0), y1), y2)), z1))) MARK(and(and(s(cons(and(and(zeros, y0), y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(and(and(zeros, y0), y1), y2)), z1))) MARK(and(and(s(cons(length(and(and(y0, y1), y2)), y3)), z1), z2)) -> c8(MARK(and(s(cons(length(and(and(y0, y1), y2)), y3)), z1))) MARK(and(and(s(cons(length(and(length(y0), y1)), y2)), z1), z2)) -> c8(MARK(and(s(cons(length(and(length(y0), y1)), y2)), z1))) MARK(and(and(s(cons(length(and(cons(y0, y1), y2)), y3)), z1), z2)) -> c8(MARK(and(s(cons(length(and(cons(y0, y1), y2)), y3)), z1))) MARK(and(and(s(cons(length(and(tt, y0)), y1)), z1), z2)) -> c8(MARK(and(s(cons(length(and(tt, y0)), y1)), z1))) MARK(and(and(s(cons(length(and(s(y0), y1)), y2)), z1), z2)) -> c8(MARK(and(s(cons(length(and(s(y0), y1)), y2)), z1))) MARK(and(and(s(cons(length(and(y0, y1)), y2)), z1), z2)) -> c8(MARK(and(s(cons(length(and(y0, y1)), y2)), z1))) MARK(and(and(s(cons(length(and(zeros, y0)), y1)), z1), z2)) -> c8(MARK(and(s(cons(length(and(zeros, y0)), y1)), z1))) MARK(and(and(s(cons(length(length(zeros)), y0)), z1), z2)) -> c8(MARK(and(s(cons(length(length(zeros)), y0)), z1))) MARK(and(and(s(cons(length(length(and(y0, y1))), y2)), z1), z2)) -> c8(MARK(and(s(cons(length(length(and(y0, y1))), y2)), z1))) MARK(and(and(s(cons(length(length(length(y0))), y1)), z1), z2)) -> c8(MARK(and(s(cons(length(length(length(y0))), y1)), z1))) MARK(and(and(s(cons(length(length(cons(y0, y1))), y2)), z1), z2)) -> c8(MARK(and(s(cons(length(length(cons(y0, y1))), y2)), z1))) MARK(and(and(s(cons(length(length(s(y0))), y1)), z1), z2)) -> c8(MARK(and(s(cons(length(length(s(y0))), y1)), z1))) MARK(and(and(s(cons(length(length(y0)), y1)), z1), z2)) -> c8(MARK(and(s(cons(length(length(y0)), y1)), z1))) MARK(and(and(s(cons(length(zeros), y0)), z1), z2)) -> c8(MARK(and(s(cons(length(zeros), y0)), z1))) S tuples: A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) MARK(cons(and(and(cons(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(cons(y0, y1), y2), y3))) MARK(cons(and(and(tt, y0), y1), z1)) -> c10(MARK(and(and(tt, y0), y1))) MARK(cons(and(and(s(y0), y1), y2), z1)) -> c10(MARK(and(and(s(y0), y1), y2))) MARK(cons(and(and(y0, y1), y2), z1)) -> c10(MARK(and(and(y0, y1), y2))) MARK(cons(and(length(zeros), y0), z1)) -> c10(MARK(and(length(zeros), y0))) MARK(cons(and(length(and(y0, y1)), y2), z1)) -> c10(MARK(and(length(and(y0, y1)), y2))) MARK(cons(and(length(length(y0)), y1), z1)) -> c10(MARK(and(length(length(y0)), y1))) MARK(cons(and(length(cons(y0, y1)), y2), z1)) -> c10(MARK(and(length(cons(y0, y1)), y2))) MARK(cons(and(length(s(y0)), y1), z1)) -> c10(MARK(and(length(s(y0)), y1))) MARK(cons(and(length(y0), y1), z1)) -> c10(MARK(and(length(y0), y1))) MARK(cons(and(and(zeros, y0), y1), z1)) -> c10(MARK(and(and(zeros, y0), y1))) MARK(cons(length(and(and(y0, y1), y2)), z1)) -> c10(MARK(length(and(and(y0, y1), y2)))) MARK(cons(length(and(length(y0), y1)), z1)) -> c10(MARK(length(and(length(y0), y1)))) MARK(cons(length(and(cons(y0, y1), y2)), z1)) -> c10(MARK(length(and(cons(y0, y1), y2)))) MARK(cons(length(and(tt, y0)), z1)) -> c10(MARK(length(and(tt, 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y1), z1))) MARK(and(and(and(y0, y1), z1), z2)) -> c8(MARK(and(and(y0, y1), z1))) MARK(and(and(length(zeros), z1), z2)) -> c8(MARK(and(length(zeros), z1))) MARK(and(and(length(and(y0, y1)), z1), z2)) -> c8(MARK(and(length(and(y0, y1)), z1))) MARK(and(and(length(length(y0)), z1), z2)) -> c8(MARK(and(length(length(y0)), z1))) MARK(and(and(length(cons(y0, y1)), z1), z2)) -> c8(MARK(and(length(cons(y0, y1)), z1))) MARK(and(and(length(s(y0)), z1), z2)) -> c8(MARK(and(length(s(y0)), z1))) MARK(and(and(length(y0), z1), z2)) -> c8(MARK(and(length(y0), z1))) MARK(and(and(and(zeros, y0), z1), z2)) -> c8(MARK(and(and(zeros, y0), z1))) MARK(and(and(cons(cons(y0, y1), y2), z1), z2)) -> c8(MARK(and(cons(cons(y0, y1), y2), z1))) MARK(and(and(cons(s(y0), y1), z1), z2)) -> c8(MARK(and(cons(s(y0), y1), z1))) MARK(and(and(cons(and(cons(y0, y1), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(cons(y0, y1), y2), y3), z1))) MARK(and(and(cons(and(tt, y0), y1), z1), z2)) -> c8(MARK(and(cons(and(tt, y0), y1), z1))) MARK(and(and(cons(and(s(y0), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(s(y0), y1), y2), z1))) MARK(and(and(cons(length(cons(y0, y1)), y2), z1), z2)) -> c8(MARK(and(cons(length(cons(y0, y1)), y2), z1))) MARK(and(and(cons(length(s(y0)), y1), z1), z2)) -> c8(MARK(and(cons(length(s(y0)), y1), z1))) MARK(and(and(cons(and(and(and(y0, y1), y2), y3), y4), z1), z2)) -> c8(MARK(and(cons(and(and(and(y0, y1), y2), y3), y4), z1))) MARK(and(and(cons(and(and(length(y0), y1), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(and(length(y0), y1), y2), y3), z1))) MARK(and(and(cons(and(and(cons(y0, y1), y2), y3), y4), z1), z2)) -> c8(MARK(and(cons(and(and(cons(y0, y1), y2), y3), y4), z1))) MARK(and(and(cons(and(and(tt, y0), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(and(tt, y0), y1), y2), z1))) MARK(and(and(cons(and(and(s(y0), y1), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(and(s(y0), y1), y2), y3), z1))) MARK(and(and(cons(and(and(y0, y1), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(and(y0, y1), y2), y3), z1))) MARK(and(and(cons(and(length(zeros), y0), y1), z1), z2)) -> c8(MARK(and(cons(and(length(zeros), y0), y1), z1))) MARK(and(and(cons(and(length(and(y0, y1)), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(length(and(y0, y1)), y2), y3), z1))) MARK(and(and(cons(and(length(length(y0)), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(length(length(y0)), y1), y2), z1))) MARK(and(and(cons(and(length(cons(y0, y1)), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(length(cons(y0, y1)), y2), y3), z1))) MARK(and(and(cons(and(length(s(y0)), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(length(s(y0)), y1), y2), z1))) MARK(and(and(cons(and(length(y0), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(length(y0), y1), y2), z1))) MARK(and(and(cons(and(and(zeros, y0), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(and(zeros, y0), y1), y2), z1))) MARK(and(and(cons(length(and(and(y0, y1), y2)), y3), z1), z2)) -> c8(MARK(and(cons(length(and(and(y0, y1), y2)), y3), z1))) MARK(and(and(cons(length(and(length(y0), y1)), y2), z1), z2)) -> c8(MARK(and(cons(length(and(length(y0), y1)), y2), z1))) MARK(and(and(cons(length(and(cons(y0, y1), y2)), y3), z1), z2)) -> c8(MARK(and(cons(length(and(cons(y0, y1), y2)), y3), z1))) MARK(and(and(cons(length(and(tt, y0)), y1), z1), z2)) -> c8(MARK(and(cons(length(and(tt, y0)), y1), z1))) MARK(and(and(cons(length(and(s(y0), y1)), y2), z1), z2)) -> c8(MARK(and(cons(length(and(s(y0), y1)), y2), z1))) MARK(and(and(cons(length(and(y0, y1)), y2), z1), z2)) -> c8(MARK(and(cons(length(and(y0, y1)), y2), z1))) MARK(and(and(cons(length(and(zeros, y0)), y1), z1), z2)) -> c8(MARK(and(cons(length(and(zeros, y0)), y1), z1))) MARK(and(and(cons(length(length(zeros)), y0), z1), z2)) -> c8(MARK(and(cons(length(length(zeros)), y0), z1))) MARK(and(and(cons(length(length(and(y0, y1))), y2), z1), z2)) -> c8(MARK(and(cons(length(length(and(y0, y1))), y2), z1))) MARK(and(and(cons(length(length(length(y0))), y1), z1), z2)) -> c8(MARK(and(cons(length(length(length(y0))), y1), z1))) MARK(and(and(cons(length(length(cons(y0, y1))), y2), z1), z2)) -> c8(MARK(and(cons(length(length(cons(y0, y1))), y2), z1))) MARK(and(and(cons(length(length(s(y0))), y1), z1), z2)) -> c8(MARK(and(cons(length(length(s(y0))), y1), z1))) MARK(and(and(cons(length(length(y0)), y1), z1), z2)) -> c8(MARK(and(cons(length(length(y0)), y1), z1))) MARK(and(and(cons(length(zeros), y0), z1), z2)) -> c8(MARK(and(cons(length(zeros), y0), z1))) MARK(and(and(tt, cons(y0, y1)), z2)) -> c8(MARK(and(tt, cons(y0, y1)))) MARK(and(and(tt, s(y0)), z2)) -> c8(MARK(and(tt, s(y0)))) MARK(and(and(tt, and(cons(y0, y1), y2)), z2)) -> c8(MARK(and(tt, and(cons(y0, y1), y2)))) MARK(and(and(tt, and(tt, y0)), z2)) -> c8(MARK(and(tt, and(tt, y0)))) MARK(and(and(tt, and(s(y0), y1)), z2)) -> c8(MARK(and(tt, and(s(y0), y1)))) MARK(and(and(tt, length(cons(y0, y1))), z2)) -> c8(MARK(and(tt, length(cons(y0, y1))))) MARK(and(and(tt, length(s(y0))), z2)) -> c8(MARK(and(tt, length(s(y0))))) MARK(and(and(tt, and(and(and(y0, y1), y2), y3)), z2)) -> c8(MARK(and(tt, and(and(and(y0, y1), y2), y3)))) MARK(and(and(tt, and(and(length(y0), y1), y2)), z2)) -> c8(MARK(and(tt, and(and(length(y0), y1), y2)))) MARK(and(and(tt, and(and(cons(y0, y1), y2), y3)), z2)) -> c8(MARK(and(tt, and(and(cons(y0, y1), y2), y3)))) MARK(and(and(tt, and(and(tt, y0), y1)), z2)) -> c8(MARK(and(tt, and(and(tt, y0), y1)))) MARK(and(and(tt, and(and(s(y0), y1), y2)), z2)) -> c8(MARK(and(tt, and(and(s(y0), y1), y2)))) MARK(and(and(tt, and(and(y0, y1), y2)), z2)) -> c8(MARK(and(tt, and(and(y0, y1), y2)))) MARK(and(and(tt, and(length(zeros), y0)), z2)) -> c8(MARK(and(tt, and(length(zeros), y0)))) MARK(and(and(tt, and(length(and(y0, y1)), y2)), z2)) -> c8(MARK(and(tt, and(length(and(y0, y1)), y2)))) MARK(and(and(tt, and(length(length(y0)), y1)), z2)) -> c8(MARK(and(tt, and(length(length(y0)), y1)))) MARK(and(and(tt, and(length(cons(y0, y1)), y2)), z2)) -> c8(MARK(and(tt, and(length(cons(y0, y1)), y2)))) MARK(and(and(tt, and(length(s(y0)), y1)), z2)) -> c8(MARK(and(tt, and(length(s(y0)), y1)))) MARK(and(and(tt, and(length(y0), y1)), z2)) -> c8(MARK(and(tt, and(length(y0), y1)))) MARK(and(and(tt, and(and(zeros, y0), y1)), z2)) -> c8(MARK(and(tt, and(and(zeros, y0), y1)))) MARK(and(and(tt, length(and(and(y0, y1), y2))), z2)) -> c8(MARK(and(tt, length(and(and(y0, y1), y2))))) MARK(and(and(tt, length(and(length(y0), y1))), z2)) -> c8(MARK(and(tt, length(and(length(y0), y1))))) MARK(and(and(tt, length(and(cons(y0, y1), y2))), z2)) -> c8(MARK(and(tt, length(and(cons(y0, y1), y2))))) MARK(and(and(tt, length(and(tt, y0))), z2)) -> c8(MARK(and(tt, length(and(tt, y0))))) MARK(and(and(tt, length(and(s(y0), y1))), z2)) -> c8(MARK(and(tt, length(and(s(y0), y1))))) MARK(and(and(tt, length(and(y0, y1))), z2)) -> c8(MARK(and(tt, length(and(y0, y1))))) MARK(and(and(tt, length(and(zeros, y0))), z2)) -> c8(MARK(and(tt, length(and(zeros, y0))))) MARK(and(and(tt, length(length(zeros))), z2)) -> c8(MARK(and(tt, length(length(zeros))))) MARK(and(and(tt, length(length(and(y0, y1)))), z2)) -> c8(MARK(and(tt, length(length(and(y0, y1)))))) MARK(and(and(tt, length(length(length(y0)))), z2)) -> c8(MARK(and(tt, length(length(length(y0)))))) MARK(and(and(tt, length(length(cons(y0, y1)))), z2)) -> c8(MARK(and(tt, length(length(cons(y0, y1)))))) MARK(and(and(tt, length(length(s(y0)))), z2)) -> c8(MARK(and(tt, length(length(s(y0)))))) MARK(and(and(tt, length(length(y0))), z2)) -> c8(MARK(and(tt, length(length(y0))))) MARK(and(and(tt, length(zeros)), z2)) -> c8(MARK(and(tt, length(zeros)))) MARK(and(and(s(s(y0)), z1), z2)) -> c8(MARK(and(s(s(y0)), z1))) MARK(and(and(s(and(cons(y0, y1), y2)), z1), z2)) -> c8(MARK(and(s(and(cons(y0, y1), y2)), z1))) MARK(and(and(s(and(tt, y0)), z1), z2)) -> c8(MARK(and(s(and(tt, y0)), z1))) MARK(and(and(s(and(s(y0), y1)), z1), z2)) -> c8(MARK(and(s(and(s(y0), y1)), z1))) MARK(and(and(s(length(cons(y0, y1))), z1), z2)) -> c8(MARK(and(s(length(cons(y0, y1))), z1))) MARK(and(and(s(length(s(y0))), z1), z2)) -> c8(MARK(and(s(length(s(y0))), z1))) MARK(and(and(s(and(and(and(y0, y1), y2), y3)), z1), z2)) -> c8(MARK(and(s(and(and(and(y0, y1), y2), y3)), z1))) MARK(and(and(s(and(and(length(y0), y1), y2)), z1), z2)) -> c8(MARK(and(s(and(and(length(y0), y1), y2)), z1))) MARK(and(and(s(and(and(cons(y0, y1), y2), y3)), z1), z2)) -> c8(MARK(and(s(and(and(cons(y0, y1), y2), y3)), z1))) MARK(and(and(s(and(and(tt, y0), y1)), z1), z2)) -> c8(MARK(and(s(and(and(tt, y0), y1)), z1))) MARK(and(and(s(and(and(s(y0), y1), y2)), z1), z2)) -> c8(MARK(and(s(and(and(s(y0), y1), y2)), z1))) MARK(and(and(s(and(and(y0, y1), y2)), z1), z2)) -> c8(MARK(and(s(and(and(y0, y1), y2)), z1))) MARK(and(and(s(and(length(zeros), y0)), z1), z2)) -> c8(MARK(and(s(and(length(zeros), y0)), z1))) MARK(and(and(s(and(length(and(y0, y1)), y2)), z1), z2)) -> c8(MARK(and(s(and(length(and(y0, y1)), y2)), z1))) MARK(and(and(s(and(length(length(y0)), y1)), z1), z2)) -> c8(MARK(and(s(and(length(length(y0)), y1)), z1))) MARK(and(and(s(and(length(cons(y0, y1)), y2)), z1), z2)) -> c8(MARK(and(s(and(length(cons(y0, y1)), y2)), z1))) MARK(and(and(s(and(length(s(y0)), y1)), z1), z2)) -> c8(MARK(and(s(and(length(s(y0)), y1)), z1))) MARK(and(and(s(and(length(y0), y1)), z1), z2)) -> c8(MARK(and(s(and(length(y0), y1)), z1))) MARK(and(and(s(and(and(zeros, y0), y1)), z1), z2)) -> c8(MARK(and(s(and(and(zeros, y0), y1)), z1))) MARK(and(and(s(length(and(and(y0, y1), y2))), z1), z2)) -> c8(MARK(and(s(length(and(and(y0, y1), y2))), z1))) MARK(and(and(s(length(and(length(y0), y1))), z1), z2)) -> c8(MARK(and(s(length(and(length(y0), y1))), z1))) MARK(and(and(s(length(and(cons(y0, y1), y2))), z1), z2)) -> c8(MARK(and(s(length(and(cons(y0, y1), y2))), z1))) MARK(and(and(s(length(and(tt, y0))), z1), z2)) -> c8(MARK(and(s(length(and(tt, y0))), z1))) MARK(and(and(s(length(and(s(y0), y1))), z1), z2)) -> c8(MARK(and(s(length(and(s(y0), y1))), z1))) MARK(and(and(s(length(and(y0, y1))), z1), z2)) -> c8(MARK(and(s(length(and(y0, y1))), z1))) MARK(and(and(s(length(and(zeros, y0))), z1), z2)) -> c8(MARK(and(s(length(and(zeros, y0))), z1))) MARK(and(and(s(length(length(zeros))), z1), z2)) -> c8(MARK(and(s(length(length(zeros))), z1))) MARK(and(and(s(length(length(and(y0, y1)))), z1), z2)) -> c8(MARK(and(s(length(length(and(y0, y1)))), z1))) MARK(and(and(s(length(length(length(y0)))), z1), z2)) -> c8(MARK(and(s(length(length(length(y0)))), z1))) MARK(and(and(s(length(length(cons(y0, y1)))), z1), z2)) -> c8(MARK(and(s(length(length(cons(y0, y1)))), z1))) MARK(and(and(s(length(length(s(y0)))), z1), z2)) -> c8(MARK(and(s(length(length(s(y0)))), z1))) MARK(and(and(s(length(length(y0))), z1), z2)) -> c8(MARK(and(s(length(length(y0))), z1))) MARK(and(and(s(length(zeros)), z1), z2)) -> c8(MARK(and(s(length(zeros)), z1))) MARK(and(and(s(cons(cons(y0, y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(cons(y0, y1), y2)), z1))) MARK(and(and(s(cons(s(y0), y1)), z1), z2)) -> c8(MARK(and(s(cons(s(y0), y1)), z1))) MARK(and(and(s(cons(and(cons(y0, y1), y2), y3)), z1), z2)) -> c8(MARK(and(s(cons(and(cons(y0, y1), y2), y3)), z1))) MARK(and(and(s(cons(and(tt, y0), y1)), z1), z2)) -> c8(MARK(and(s(cons(and(tt, y0), y1)), z1))) MARK(and(and(s(cons(and(s(y0), y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(and(s(y0), y1), y2)), z1))) MARK(and(and(s(cons(length(cons(y0, y1)), y2)), z1), z2)) -> c8(MARK(and(s(cons(length(cons(y0, y1)), y2)), z1))) MARK(and(and(s(cons(length(s(y0)), y1)), z1), z2)) -> c8(MARK(and(s(cons(length(s(y0)), y1)), z1))) MARK(and(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), z1), z2)) -> c8(MARK(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), z1))) MARK(and(and(s(cons(and(and(length(y0), y1), y2), y3)), z1), z2)) -> c8(MARK(and(s(cons(and(and(length(y0), y1), y2), y3)), z1))) MARK(and(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), z1), z2)) -> c8(MARK(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), z1))) MARK(and(and(s(cons(and(and(tt, y0), y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(and(and(tt, y0), y1), y2)), z1))) MARK(and(and(s(cons(and(and(s(y0), y1), y2), y3)), z1), z2)) -> c8(MARK(and(s(cons(and(and(s(y0), y1), y2), y3)), z1))) MARK(and(and(s(cons(and(and(y0, y1), y2), y3)), z1), z2)) -> c8(MARK(and(s(cons(and(and(y0, y1), y2), y3)), z1))) MARK(and(and(s(cons(and(length(zeros), y0), y1)), z1), z2)) -> c8(MARK(and(s(cons(and(length(zeros), y0), y1)), z1))) MARK(and(and(s(cons(and(length(and(y0, y1)), y2), y3)), z1), z2)) -> c8(MARK(and(s(cons(and(length(and(y0, y1)), y2), y3)), z1))) MARK(and(and(s(cons(and(length(length(y0)), y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(and(length(length(y0)), y1), y2)), z1))) MARK(and(and(s(cons(and(length(cons(y0, y1)), y2), y3)), z1), z2)) -> c8(MARK(and(s(cons(and(length(cons(y0, y1)), y2), y3)), z1))) MARK(and(and(s(cons(and(length(s(y0)), y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(and(length(s(y0)), y1), y2)), z1))) MARK(and(and(s(cons(and(length(y0), y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(and(length(y0), y1), y2)), z1))) MARK(and(and(s(cons(and(and(zeros, y0), y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(and(and(zeros, y0), y1), y2)), z1))) MARK(and(and(s(cons(length(and(and(y0, y1), y2)), y3)), z1), z2)) -> c8(MARK(and(s(cons(length(and(and(y0, y1), y2)), y3)), z1))) MARK(and(and(s(cons(length(and(length(y0), y1)), y2)), z1), z2)) -> c8(MARK(and(s(cons(length(and(length(y0), y1)), y2)), z1))) MARK(and(and(s(cons(length(and(cons(y0, y1), y2)), y3)), z1), z2)) -> c8(MARK(and(s(cons(length(and(cons(y0, y1), y2)), y3)), z1))) MARK(and(and(s(cons(length(and(tt, y0)), y1)), z1), z2)) -> c8(MARK(and(s(cons(length(and(tt, y0)), y1)), z1))) MARK(and(and(s(cons(length(and(s(y0), y1)), y2)), z1), z2)) -> c8(MARK(and(s(cons(length(and(s(y0), y1)), y2)), z1))) MARK(and(and(s(cons(length(and(y0, y1)), y2)), z1), z2)) -> c8(MARK(and(s(cons(length(and(y0, y1)), y2)), z1))) MARK(and(and(s(cons(length(and(zeros, y0)), y1)), z1), z2)) -> c8(MARK(and(s(cons(length(and(zeros, y0)), y1)), z1))) MARK(and(and(s(cons(length(length(zeros)), y0)), z1), z2)) -> c8(MARK(and(s(cons(length(length(zeros)), y0)), z1))) MARK(and(and(s(cons(length(length(and(y0, y1))), y2)), z1), z2)) -> c8(MARK(and(s(cons(length(length(and(y0, y1))), y2)), z1))) MARK(and(and(s(cons(length(length(length(y0))), y1)), z1), z2)) -> c8(MARK(and(s(cons(length(length(length(y0))), y1)), z1))) MARK(and(and(s(cons(length(length(cons(y0, y1))), y2)), z1), z2)) -> c8(MARK(and(s(cons(length(length(cons(y0, y1))), y2)), z1))) MARK(and(and(s(cons(length(length(s(y0))), y1)), z1), z2)) -> c8(MARK(and(s(cons(length(length(s(y0))), y1)), z1))) MARK(and(and(s(cons(length(length(y0)), y1)), z1), z2)) -> c8(MARK(and(s(cons(length(length(y0)), y1)), z1))) MARK(and(and(s(cons(length(zeros), y0)), z1), z2)) -> c8(MARK(and(s(cons(length(zeros), y0)), z1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__LENGTH_1, MARK_1, A__AND_2 Compound Symbols: c5_2, c9_2, c5_1, c8_2, c8_1, c9_1, c2_1, c10_1, c14_1 ---------------------------------------- (187) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(and(length(x0), x1)) -> c8(MARK(length(x0))) by MARK(and(length(cons(y0, y1)), z1)) -> c8(MARK(length(cons(y0, y1)))) MARK(and(length(and(and(y0, y1), y2)), z1)) -> c8(MARK(length(and(and(y0, y1), y2)))) MARK(and(length(and(length(y0), y1)), z1)) -> c8(MARK(length(and(length(y0), y1)))) MARK(and(length(and(cons(y0, y1), y2)), z1)) -> c8(MARK(length(and(cons(y0, y1), y2)))) MARK(and(length(and(tt, y0)), z1)) -> c8(MARK(length(and(tt, y0)))) MARK(and(length(and(s(y0), y1)), z1)) -> c8(MARK(length(and(s(y0), y1)))) MARK(and(length(and(y0, y1)), z1)) -> c8(MARK(length(and(y0, y1)))) MARK(and(length(and(zeros, y0)), z1)) -> c8(MARK(length(and(zeros, y0)))) MARK(and(length(length(zeros)), z1)) -> c8(MARK(length(length(zeros)))) MARK(and(length(length(and(y0, y1))), z1)) -> c8(MARK(length(length(and(y0, y1))))) MARK(and(length(length(length(y0))), z1)) -> c8(MARK(length(length(length(y0))))) MARK(and(length(length(cons(y0, y1))), z1)) -> c8(MARK(length(length(cons(y0, y1))))) MARK(and(length(length(s(y0))), z1)) -> c8(MARK(length(length(s(y0))))) MARK(and(length(length(y0)), z1)) -> c8(MARK(length(length(y0)))) MARK(and(length(zeros), z1)) -> c8(MARK(length(zeros))) MARK(and(length(s(s(y0))), z1)) -> c8(MARK(length(s(s(y0))))) MARK(and(length(s(and(cons(y0, y1), y2))), z1)) -> c8(MARK(length(s(and(cons(y0, y1), y2))))) MARK(and(length(s(and(tt, y0))), z1)) -> c8(MARK(length(s(and(tt, y0))))) MARK(and(length(s(and(s(y0), y1))), z1)) -> c8(MARK(length(s(and(s(y0), y1))))) MARK(and(length(s(length(cons(y0, y1)))), z1)) -> c8(MARK(length(s(length(cons(y0, y1)))))) MARK(and(length(s(length(s(y0)))), z1)) -> c8(MARK(length(s(length(s(y0)))))) MARK(and(length(s(and(and(and(y0, y1), y2), y3))), z1)) -> c8(MARK(length(s(and(and(and(y0, y1), y2), y3))))) MARK(and(length(s(and(and(length(y0), y1), y2))), z1)) -> c8(MARK(length(s(and(and(length(y0), y1), y2))))) MARK(and(length(s(and(and(cons(y0, y1), y2), y3))), z1)) -> c8(MARK(length(s(and(and(cons(y0, y1), y2), y3))))) MARK(and(length(s(and(and(tt, y0), y1))), z1)) -> c8(MARK(length(s(and(and(tt, y0), y1))))) MARK(and(length(s(and(and(s(y0), y1), y2))), z1)) -> c8(MARK(length(s(and(and(s(y0), y1), y2))))) MARK(and(length(s(and(and(y0, y1), y2))), z1)) -> c8(MARK(length(s(and(and(y0, y1), y2))))) MARK(and(length(s(and(length(zeros), y0))), z1)) -> c8(MARK(length(s(and(length(zeros), y0))))) MARK(and(length(s(and(length(and(y0, y1)), y2))), z1)) -> c8(MARK(length(s(and(length(and(y0, y1)), y2))))) MARK(and(length(s(and(length(length(y0)), y1))), z1)) -> c8(MARK(length(s(and(length(length(y0)), y1))))) MARK(and(length(s(and(length(cons(y0, y1)), y2))), z1)) -> c8(MARK(length(s(and(length(cons(y0, y1)), y2))))) MARK(and(length(s(and(length(s(y0)), y1))), z1)) -> c8(MARK(length(s(and(length(s(y0)), y1))))) MARK(and(length(s(and(length(y0), y1))), z1)) -> c8(MARK(length(s(and(length(y0), y1))))) MARK(and(length(s(and(and(zeros, y0), y1))), z1)) -> c8(MARK(length(s(and(and(zeros, y0), y1))))) MARK(and(length(s(length(and(and(y0, y1), y2)))), z1)) -> c8(MARK(length(s(length(and(and(y0, y1), y2)))))) MARK(and(length(s(length(and(length(y0), y1)))), z1)) -> c8(MARK(length(s(length(and(length(y0), y1)))))) MARK(and(length(s(length(and(cons(y0, y1), y2)))), z1)) -> c8(MARK(length(s(length(and(cons(y0, y1), y2)))))) MARK(and(length(s(length(and(tt, y0)))), z1)) -> c8(MARK(length(s(length(and(tt, y0)))))) MARK(and(length(s(length(and(s(y0), y1)))), z1)) -> c8(MARK(length(s(length(and(s(y0), y1)))))) MARK(and(length(s(length(and(y0, y1)))), z1)) -> c8(MARK(length(s(length(and(y0, y1)))))) MARK(and(length(s(length(and(zeros, y0)))), z1)) -> c8(MARK(length(s(length(and(zeros, y0)))))) MARK(and(length(s(length(length(zeros)))), z1)) -> c8(MARK(length(s(length(length(zeros)))))) MARK(and(length(s(length(length(and(y0, y1))))), z1)) -> c8(MARK(length(s(length(length(and(y0, y1))))))) MARK(and(length(s(length(length(length(y0))))), z1)) -> c8(MARK(length(s(length(length(length(y0))))))) MARK(and(length(s(length(length(cons(y0, y1))))), z1)) -> c8(MARK(length(s(length(length(cons(y0, y1))))))) MARK(and(length(s(length(length(s(y0))))), z1)) -> c8(MARK(length(s(length(length(s(y0))))))) MARK(and(length(s(length(length(y0)))), z1)) -> c8(MARK(length(s(length(length(y0)))))) MARK(and(length(s(length(zeros))), z1)) -> c8(MARK(length(s(length(zeros))))) MARK(and(length(s(cons(cons(y0, y1), y2))), z1)) -> c8(MARK(length(s(cons(cons(y0, y1), y2))))) MARK(and(length(s(cons(s(y0), y1))), z1)) -> c8(MARK(length(s(cons(s(y0), y1))))) MARK(and(length(s(cons(and(cons(y0, y1), y2), y3))), z1)) -> c8(MARK(length(s(cons(and(cons(y0, y1), y2), y3))))) MARK(and(length(s(cons(and(tt, y0), y1))), z1)) -> c8(MARK(length(s(cons(and(tt, y0), y1))))) MARK(and(length(s(cons(and(s(y0), y1), y2))), z1)) -> c8(MARK(length(s(cons(and(s(y0), y1), y2))))) MARK(and(length(s(cons(length(cons(y0, y1)), y2))), z1)) -> c8(MARK(length(s(cons(length(cons(y0, y1)), y2))))) MARK(and(length(s(cons(length(s(y0)), y1))), z1)) -> c8(MARK(length(s(cons(length(s(y0)), y1))))) MARK(and(length(s(cons(and(and(and(y0, y1), y2), y3), y4))), z1)) -> c8(MARK(length(s(cons(and(and(and(y0, y1), y2), y3), y4))))) MARK(and(length(s(cons(and(and(length(y0), y1), y2), y3))), z1)) -> c8(MARK(length(s(cons(and(and(length(y0), y1), y2), y3))))) MARK(and(length(s(cons(and(and(cons(y0, y1), y2), y3), y4))), z1)) -> c8(MARK(length(s(cons(and(and(cons(y0, y1), y2), y3), y4))))) MARK(and(length(s(cons(and(and(tt, y0), y1), y2))), z1)) -> c8(MARK(length(s(cons(and(and(tt, y0), y1), y2))))) MARK(and(length(s(cons(and(and(s(y0), y1), y2), y3))), z1)) -> c8(MARK(length(s(cons(and(and(s(y0), y1), y2), y3))))) MARK(and(length(s(cons(and(and(y0, y1), y2), y3))), z1)) -> c8(MARK(length(s(cons(and(and(y0, y1), y2), y3))))) MARK(and(length(s(cons(and(length(zeros), y0), y1))), z1)) -> c8(MARK(length(s(cons(and(length(zeros), y0), y1))))) MARK(and(length(s(cons(and(length(and(y0, y1)), y2), y3))), z1)) -> c8(MARK(length(s(cons(and(length(and(y0, y1)), y2), y3))))) MARK(and(length(s(cons(and(length(length(y0)), y1), y2))), z1)) -> c8(MARK(length(s(cons(and(length(length(y0)), y1), y2))))) MARK(and(length(s(cons(and(length(cons(y0, y1)), y2), y3))), z1)) -> c8(MARK(length(s(cons(and(length(cons(y0, y1)), y2), y3))))) MARK(and(length(s(cons(and(length(s(y0)), y1), y2))), z1)) -> c8(MARK(length(s(cons(and(length(s(y0)), y1), y2))))) MARK(and(length(s(cons(and(length(y0), y1), y2))), z1)) -> c8(MARK(length(s(cons(and(length(y0), y1), y2))))) MARK(and(length(s(cons(and(and(zeros, y0), y1), y2))), z1)) -> c8(MARK(length(s(cons(and(and(zeros, y0), y1), y2))))) MARK(and(length(s(cons(length(and(and(y0, y1), y2)), y3))), z1)) -> c8(MARK(length(s(cons(length(and(and(y0, y1), y2)), y3))))) MARK(and(length(s(cons(length(and(length(y0), y1)), y2))), z1)) -> c8(MARK(length(s(cons(length(and(length(y0), y1)), y2))))) MARK(and(length(s(cons(length(and(cons(y0, y1), y2)), y3))), z1)) -> c8(MARK(length(s(cons(length(and(cons(y0, y1), y2)), y3))))) MARK(and(length(s(cons(length(and(tt, y0)), y1))), z1)) -> c8(MARK(length(s(cons(length(and(tt, y0)), y1))))) MARK(and(length(s(cons(length(and(s(y0), y1)), y2))), z1)) -> c8(MARK(length(s(cons(length(and(s(y0), y1)), y2))))) MARK(and(length(s(cons(length(and(y0, y1)), y2))), z1)) -> c8(MARK(length(s(cons(length(and(y0, y1)), y2))))) MARK(and(length(s(cons(length(and(zeros, y0)), y1))), z1)) -> c8(MARK(length(s(cons(length(and(zeros, y0)), y1))))) MARK(and(length(s(cons(length(length(zeros)), y0))), z1)) -> c8(MARK(length(s(cons(length(length(zeros)), y0))))) MARK(and(length(s(cons(length(length(and(y0, y1))), y2))), z1)) -> c8(MARK(length(s(cons(length(length(and(y0, y1))), y2))))) MARK(and(length(s(cons(length(length(length(y0))), y1))), z1)) -> c8(MARK(length(s(cons(length(length(length(y0))), y1))))) MARK(and(length(s(cons(length(length(cons(y0, y1))), y2))), z1)) -> c8(MARK(length(s(cons(length(length(cons(y0, y1))), y2))))) MARK(and(length(s(cons(length(length(s(y0))), y1))), z1)) -> c8(MARK(length(s(cons(length(length(s(y0))), y1))))) MARK(and(length(s(cons(length(length(y0)), y1))), z1)) -> c8(MARK(length(s(cons(length(length(y0)), y1))))) MARK(and(length(s(cons(length(zeros), y0))), z1)) -> c8(MARK(length(s(cons(length(zeros), y0))))) ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) MARK(cons(and(and(cons(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(cons(y0, y1), y2), y3))) MARK(cons(and(and(tt, y0), y1), z1)) -> c10(MARK(and(and(tt, y0), y1))) MARK(cons(and(and(s(y0), y1), y2), z1)) -> c10(MARK(and(and(s(y0), y1), y2))) MARK(cons(and(and(y0, y1), y2), z1)) -> c10(MARK(and(and(y0, y1), y2))) MARK(cons(and(length(zeros), y0), z1)) -> c10(MARK(and(length(zeros), y0))) MARK(cons(and(length(and(y0, y1)), y2), z1)) -> c10(MARK(and(length(and(y0, y1)), y2))) MARK(cons(and(length(length(y0)), y1), z1)) -> c10(MARK(and(length(length(y0)), y1))) MARK(cons(and(length(cons(y0, y1)), y2), z1)) -> c10(MARK(and(length(cons(y0, y1)), y2))) MARK(cons(and(length(s(y0)), y1), z1)) -> c10(MARK(and(length(s(y0)), y1))) MARK(cons(and(length(y0), y1), z1)) -> c10(MARK(and(length(y0), y1))) MARK(cons(and(and(zeros, y0), y1), z1)) -> c10(MARK(and(and(zeros, y0), y1))) MARK(cons(length(and(and(y0, y1), y2)), z1)) -> c10(MARK(length(and(and(y0, y1), y2)))) MARK(cons(length(and(length(y0), y1)), z1)) -> c10(MARK(length(and(length(y0), y1)))) MARK(cons(length(and(cons(y0, y1), y2)), z1)) -> c10(MARK(length(and(cons(y0, y1), y2)))) MARK(cons(length(and(tt, y0)), z1)) -> c10(MARK(length(and(tt, y0)))) MARK(cons(length(and(s(y0), y1)), z1)) -> c10(MARK(length(and(s(y0), y1)))) MARK(cons(length(and(y0, y1)), z1)) -> c10(MARK(length(and(y0, y1)))) MARK(cons(length(and(zeros, y0)), z1)) -> c10(MARK(length(and(zeros, y0)))) MARK(cons(length(length(zeros)), z1)) -> c10(MARK(length(length(zeros)))) MARK(cons(length(length(and(y0, y1))), z1)) -> c10(MARK(length(length(and(y0, y1))))) MARK(cons(length(length(length(y0))), z1)) -> c10(MARK(length(length(length(y0))))) MARK(cons(length(length(cons(y0, y1))), z1)) -> c10(MARK(length(length(cons(y0, y1))))) MARK(cons(length(length(s(y0))), z1)) -> c10(MARK(length(length(s(y0))))) MARK(cons(length(length(y0)), z1)) -> c10(MARK(length(length(y0)))) MARK(cons(length(zeros), z1)) -> c10(MARK(length(zeros))) MARK(s(s(y0))) -> c14(MARK(s(y0))) MARK(s(and(cons(y0, y1), y2))) -> c14(MARK(and(cons(y0, y1), y2))) MARK(s(and(tt, y0))) -> c14(MARK(and(tt, y0))) MARK(s(and(s(y0), y1))) -> c14(MARK(and(s(y0), y1))) MARK(s(length(cons(y0, y1)))) -> c14(MARK(length(cons(y0, y1)))) MARK(s(length(s(y0)))) -> c14(MARK(length(s(y0)))) MARK(s(and(and(and(y0, y1), y2), y3))) -> c14(MARK(and(and(and(y0, y1), y2), y3))) MARK(s(and(and(length(y0), y1), y2))) -> c14(MARK(and(and(length(y0), y1), y2))) MARK(s(and(and(cons(y0, y1), y2), y3))) -> c14(MARK(and(and(cons(y0, y1), y2), y3))) MARK(s(and(and(tt, y0), y1))) -> c14(MARK(and(and(tt, y0), y1))) MARK(s(and(and(s(y0), y1), y2))) -> c14(MARK(and(and(s(y0), y1), y2))) MARK(s(and(and(y0, y1), y2))) -> c14(MARK(and(and(y0, y1), y2))) MARK(s(and(length(zeros), y0))) -> c14(MARK(and(length(zeros), y0))) MARK(s(and(length(and(y0, y1)), y2))) -> c14(MARK(and(length(and(y0, y1)), y2))) MARK(s(and(length(length(y0)), y1))) -> c14(MARK(and(length(length(y0)), y1))) MARK(s(and(length(cons(y0, y1)), y2))) -> c14(MARK(and(length(cons(y0, y1)), y2))) MARK(s(and(length(s(y0)), y1))) -> c14(MARK(and(length(s(y0)), y1))) MARK(s(and(length(y0), y1))) -> c14(MARK(and(length(y0), y1))) MARK(s(and(and(zeros, y0), y1))) -> c14(MARK(and(and(zeros, y0), y1))) MARK(s(length(and(and(y0, y1), y2)))) -> c14(MARK(length(and(and(y0, y1), y2)))) MARK(s(length(and(length(y0), y1)))) -> c14(MARK(length(and(length(y0), y1)))) MARK(s(length(and(cons(y0, y1), y2)))) -> c14(MARK(length(and(cons(y0, y1), y2)))) MARK(s(length(and(tt, y0)))) -> c14(MARK(length(and(tt, y0)))) MARK(s(length(and(s(y0), y1)))) -> c14(MARK(length(and(s(y0), y1)))) MARK(s(length(and(y0, y1)))) -> c14(MARK(length(and(y0, y1)))) MARK(s(length(and(zeros, y0)))) -> c14(MARK(length(and(zeros, y0)))) MARK(s(length(length(zeros)))) -> c14(MARK(length(length(zeros)))) MARK(s(length(length(and(y0, y1))))) -> c14(MARK(length(length(and(y0, y1))))) MARK(s(length(length(length(y0))))) -> c14(MARK(length(length(length(y0))))) MARK(s(length(length(cons(y0, y1))))) -> c14(MARK(length(length(cons(y0, y1))))) MARK(s(length(length(s(y0))))) -> c14(MARK(length(length(s(y0))))) MARK(s(length(length(y0)))) -> c14(MARK(length(length(y0)))) MARK(s(length(zeros))) -> c14(MARK(length(zeros))) MARK(s(cons(cons(y0, y1), y2))) -> c14(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c14(MARK(cons(s(y0), y1))) MARK(s(cons(and(cons(y0, y1), y2), y3))) -> c14(MARK(cons(and(cons(y0, y1), y2), y3))) MARK(s(cons(and(tt, y0), y1))) -> c14(MARK(cons(and(tt, y0), y1))) MARK(s(cons(and(s(y0), y1), y2))) -> c14(MARK(cons(and(s(y0), y1), y2))) MARK(s(cons(length(cons(y0, y1)), y2))) -> c14(MARK(cons(length(cons(y0, y1)), y2))) MARK(s(cons(length(s(y0)), y1))) -> c14(MARK(cons(length(s(y0)), y1))) MARK(s(cons(and(and(and(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(and(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(length(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(length(y0), y1), y2), y3))) MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(cons(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(tt, y0), y1), y2))) -> c14(MARK(cons(and(and(tt, y0), y1), y2))) MARK(s(cons(and(and(s(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(s(y0), y1), y2), y3))) MARK(s(cons(and(and(y0, y1), y2), y3))) -> c14(MARK(cons(and(and(y0, y1), y2), y3))) MARK(s(cons(and(length(zeros), y0), y1))) -> c14(MARK(cons(and(length(zeros), y0), y1))) MARK(s(cons(and(length(and(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(and(y0, y1)), y2), y3))) MARK(s(cons(and(length(length(y0)), y1), y2))) -> c14(MARK(cons(and(length(length(y0)), y1), y2))) MARK(s(cons(and(length(cons(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(cons(y0, y1)), y2), y3))) MARK(s(cons(and(length(s(y0)), y1), y2))) -> c14(MARK(cons(and(length(s(y0)), y1), y2))) MARK(s(cons(and(length(y0), y1), y2))) -> c14(MARK(cons(and(length(y0), y1), y2))) MARK(s(cons(and(and(zeros, y0), y1), y2))) -> c14(MARK(cons(and(and(zeros, y0), y1), y2))) MARK(s(cons(length(and(and(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(and(y0, 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c14(MARK(cons(length(length(s(y0))), y1))) MARK(s(cons(length(length(y0)), y1))) -> c14(MARK(cons(length(length(y0)), y1))) MARK(s(cons(length(zeros), y0))) -> c14(MARK(cons(length(zeros), y0))) A__LENGTH(cons(z0, s(s(y0)))) -> c5(MARK(s(s(y0)))) A__LENGTH(cons(z0, s(and(cons(y0, y1), y2)))) -> c5(MARK(s(and(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(tt, y0)))) -> c5(MARK(s(and(tt, y0)))) A__LENGTH(cons(z0, s(and(s(y0), y1)))) -> c5(MARK(s(and(s(y0), y1)))) A__LENGTH(cons(z0, s(length(cons(y0, y1))))) -> c5(MARK(s(length(cons(y0, y1))))) A__LENGTH(cons(z0, s(length(s(y0))))) -> c5(MARK(s(length(s(y0))))) A__LENGTH(cons(z0, s(and(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(length(y0), y1), y2)))) -> c5(MARK(s(and(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(tt, y0), y1)))) -> c5(MARK(s(and(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(and(and(s(y0), y1), y2)))) -> c5(MARK(s(and(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(y0, y1), y2)))) -> c5(MARK(s(and(and(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(length(zeros), y0)))) -> c5(MARK(s(and(length(zeros), y0)))) A__LENGTH(cons(z0, s(and(length(and(y0, y1)), y2)))) -> c5(MARK(s(and(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(length(y0)), y1)))) -> c5(MARK(s(and(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(cons(y0, y1)), y2)))) -> c5(MARK(s(and(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(s(y0)), y1)))) -> c5(MARK(s(and(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(y0), y1)))) -> c5(MARK(s(and(length(y0), y1)))) A__LENGTH(cons(z0, s(and(and(zeros, y0), y1)))) -> c5(MARK(s(and(and(zeros, y0), y1)))) A__LENGTH(cons(z0, s(length(and(and(y0, y1), y2))))) -> c5(MARK(s(length(and(and(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(length(y0), y1))))) -> c5(MARK(s(length(and(length(y0), y1))))) A__LENGTH(cons(z0, s(length(and(cons(y0, y1), y2))))) -> c5(MARK(s(length(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(tt, y0))))) -> c5(MARK(s(length(and(tt, y0))))) A__LENGTH(cons(z0, s(length(and(s(y0), y1))))) -> c5(MARK(s(length(and(s(y0), y1))))) A__LENGTH(cons(z0, s(length(and(y0, y1))))) -> c5(MARK(s(length(and(y0, y1))))) A__LENGTH(cons(z0, s(length(and(zeros, y0))))) -> c5(MARK(s(length(and(zeros, y0))))) A__LENGTH(cons(z0, s(length(length(zeros))))) -> c5(MARK(s(length(length(zeros))))) A__LENGTH(cons(z0, s(length(length(and(y0, y1)))))) -> c5(MARK(s(length(length(and(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(length(y0)))))) -> c5(MARK(s(length(length(length(y0)))))) A__LENGTH(cons(z0, s(length(length(cons(y0, y1)))))) -> c5(MARK(s(length(length(cons(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(s(y0)))))) -> c5(MARK(s(length(length(s(y0)))))) A__LENGTH(cons(z0, s(length(length(y0))))) -> c5(MARK(s(length(length(y0))))) A__LENGTH(cons(z0, 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c5(MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(tt, y0), y1), y2)))) -> c5(MARK(s(cons(and(and(tt, y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(and(s(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(s(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(zeros), y0), y1)))) -> c5(MARK(s(cons(and(length(zeros), y0), y1)))) A__LENGTH(cons(z0, s(cons(and(length(and(y0, y1)), y2), y3)))) -> c5(MARK(s(cons(and(length(and(y0, y1)), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(length(y0)), y1), y2)))) -> c5(MARK(s(cons(and(length(length(y0)), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(length(cons(y0, y1)), y2), y3)))) -> c5(MARK(s(cons(and(length(cons(y0, y1)), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(s(y0)), y1), y2)))) -> c5(MARK(s(cons(and(length(s(y0)), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(length(y0), y1), y2)))) -> 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z1)) -> c8(MARK(length(s(cons(length(length(s(y0))), y1))))) MARK(and(length(s(cons(length(length(y0)), y1))), z1)) -> c8(MARK(length(s(cons(length(length(y0)), y1))))) MARK(and(length(s(cons(length(zeros), y0))), z1)) -> c8(MARK(length(s(cons(length(zeros), y0))))) S tuples: A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, 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MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) MARK(cons(and(and(cons(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(cons(y0, y1), y2), y3))) MARK(cons(and(and(tt, y0), y1), z1)) -> c10(MARK(and(and(tt, y0), y1))) MARK(cons(and(and(s(y0), y1), y2), z1)) -> c10(MARK(and(and(s(y0), y1), y2))) MARK(cons(and(and(y0, y1), y2), z1)) -> c10(MARK(and(and(y0, y1), y2))) MARK(cons(and(length(zeros), y0), z1)) -> c10(MARK(and(length(zeros), y0))) MARK(cons(and(length(and(y0, y1)), y2), z1)) -> c10(MARK(and(length(and(y0, y1)), y2))) MARK(cons(and(length(length(y0)), y1), z1)) -> c10(MARK(and(length(length(y0)), y1))) MARK(cons(and(length(cons(y0, y1)), y2), z1)) -> c10(MARK(and(length(cons(y0, y1)), y2))) MARK(cons(and(length(s(y0)), y1), z1)) -> c10(MARK(and(length(s(y0)), y1))) MARK(cons(and(length(y0), y1), z1)) -> c10(MARK(and(length(y0), y1))) MARK(cons(and(and(zeros, y0), y1), z1)) -> c10(MARK(and(and(zeros, y0), y1))) MARK(cons(length(and(and(y0, y1), y2)), z1)) -> c10(MARK(length(and(and(y0, y1), y2)))) MARK(cons(length(and(length(y0), y1)), z1)) -> c10(MARK(length(and(length(y0), y1)))) MARK(cons(length(and(cons(y0, y1), y2)), z1)) -> c10(MARK(length(and(cons(y0, y1), y2)))) MARK(cons(length(and(tt, y0)), z1)) -> c10(MARK(length(and(tt, y0)))) MARK(cons(length(and(s(y0), y1)), z1)) -> c10(MARK(length(and(s(y0), y1)))) MARK(cons(length(and(y0, y1)), z1)) -> c10(MARK(length(and(y0, y1)))) MARK(cons(length(and(zeros, y0)), z1)) -> c10(MARK(length(and(zeros, y0)))) MARK(cons(length(length(zeros)), z1)) -> c10(MARK(length(length(zeros)))) MARK(cons(length(length(and(y0, y1))), z1)) -> c10(MARK(length(length(and(y0, y1))))) MARK(cons(length(length(length(y0))), z1)) -> c10(MARK(length(length(length(y0))))) MARK(cons(length(length(cons(y0, y1))), z1)) -> c10(MARK(length(length(cons(y0, y1))))) MARK(cons(length(length(s(y0))), z1)) -> c10(MARK(length(length(s(y0))))) MARK(cons(length(length(y0)), z1)) -> c10(MARK(length(length(y0)))) MARK(cons(length(zeros), z1)) -> c10(MARK(length(zeros))) MARK(s(s(y0))) -> c14(MARK(s(y0))) MARK(s(and(cons(y0, y1), y2))) -> c14(MARK(and(cons(y0, y1), y2))) MARK(s(and(tt, y0))) -> c14(MARK(and(tt, y0))) MARK(s(and(s(y0), y1))) -> c14(MARK(and(s(y0), y1))) MARK(s(length(cons(y0, y1)))) -> c14(MARK(length(cons(y0, y1)))) MARK(s(length(s(y0)))) -> c14(MARK(length(s(y0)))) MARK(s(and(and(and(y0, y1), y2), y3))) -> c14(MARK(and(and(and(y0, y1), y2), y3))) MARK(s(and(and(length(y0), y1), y2))) -> c14(MARK(and(and(length(y0), y1), y2))) MARK(s(and(and(cons(y0, y1), y2), y3))) -> c14(MARK(and(and(cons(y0, y1), y2), y3))) MARK(s(and(and(tt, y0), y1))) -> c14(MARK(and(and(tt, y0), y1))) MARK(s(and(and(s(y0), y1), y2))) -> c14(MARK(and(and(s(y0), y1), y2))) MARK(s(and(and(y0, y1), y2))) -> c14(MARK(and(and(y0, y1), y2))) MARK(s(and(length(zeros), y0))) -> c14(MARK(and(length(zeros), y0))) MARK(s(and(length(and(y0, y1)), y2))) -> c14(MARK(and(length(and(y0, y1)), y2))) MARK(s(and(length(length(y0)), y1))) -> c14(MARK(and(length(length(y0)), y1))) MARK(s(and(length(cons(y0, y1)), y2))) -> c14(MARK(and(length(cons(y0, y1)), y2))) MARK(s(and(length(s(y0)), y1))) -> c14(MARK(and(length(s(y0)), y1))) MARK(s(and(length(y0), y1))) -> c14(MARK(and(length(y0), y1))) MARK(s(and(and(zeros, y0), y1))) -> c14(MARK(and(and(zeros, y0), y1))) MARK(s(length(and(and(y0, y1), y2)))) -> c14(MARK(length(and(and(y0, y1), y2)))) MARK(s(length(and(length(y0), y1)))) -> c14(MARK(length(and(length(y0), y1)))) MARK(s(length(and(cons(y0, y1), y2)))) -> c14(MARK(length(and(cons(y0, y1), y2)))) MARK(s(length(and(tt, y0)))) -> c14(MARK(length(and(tt, y0)))) MARK(s(length(and(s(y0), y1)))) -> c14(MARK(length(and(s(y0), y1)))) MARK(s(length(and(y0, y1)))) -> c14(MARK(length(and(y0, y1)))) MARK(s(length(and(zeros, y0)))) -> c14(MARK(length(and(zeros, y0)))) MARK(s(length(length(zeros)))) -> c14(MARK(length(length(zeros)))) MARK(s(length(length(and(y0, y1))))) -> c14(MARK(length(length(and(y0, y1))))) MARK(s(length(length(length(y0))))) -> c14(MARK(length(length(length(y0))))) MARK(s(length(length(cons(y0, y1))))) -> c14(MARK(length(length(cons(y0, y1))))) MARK(s(length(length(s(y0))))) -> c14(MARK(length(length(s(y0))))) MARK(s(length(length(y0)))) -> c14(MARK(length(length(y0)))) MARK(s(length(zeros))) -> c14(MARK(length(zeros))) MARK(s(cons(cons(y0, y1), y2))) -> c14(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c14(MARK(cons(s(y0), y1))) MARK(s(cons(and(cons(y0, y1), y2), y3))) -> c14(MARK(cons(and(cons(y0, y1), y2), y3))) MARK(s(cons(and(tt, y0), y1))) -> c14(MARK(cons(and(tt, y0), y1))) MARK(s(cons(and(s(y0), y1), y2))) -> c14(MARK(cons(and(s(y0), y1), y2))) MARK(s(cons(length(cons(y0, y1)), y2))) -> c14(MARK(cons(length(cons(y0, y1)), y2))) MARK(s(cons(length(s(y0)), y1))) -> c14(MARK(cons(length(s(y0)), y1))) MARK(s(cons(and(and(and(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(and(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(length(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(length(y0), y1), y2), y3))) MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(cons(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(tt, y0), y1), y2))) -> c14(MARK(cons(and(and(tt, y0), y1), y2))) MARK(s(cons(and(and(s(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(s(y0), y1), y2), y3))) MARK(s(cons(and(and(y0, y1), y2), y3))) -> c14(MARK(cons(and(and(y0, y1), y2), y3))) MARK(s(cons(and(length(zeros), y0), y1))) -> c14(MARK(cons(and(length(zeros), y0), y1))) MARK(s(cons(and(length(and(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(and(y0, y1)), y2), y3))) MARK(s(cons(and(length(length(y0)), y1), y2))) -> c14(MARK(cons(and(length(length(y0)), y1), y2))) MARK(s(cons(and(length(cons(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(cons(y0, y1)), y2), y3))) MARK(s(cons(and(length(s(y0)), y1), y2))) -> c14(MARK(cons(and(length(s(y0)), y1), y2))) MARK(s(cons(and(length(y0), y1), y2))) -> c14(MARK(cons(and(length(y0), y1), y2))) MARK(s(cons(and(and(zeros, y0), y1), y2))) -> c14(MARK(cons(and(and(zeros, y0), y1), y2))) MARK(s(cons(length(and(and(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(and(y0, y1), y2)), y3))) MARK(s(cons(length(and(length(y0), y1)), y2))) -> c14(MARK(cons(length(and(length(y0), y1)), y2))) MARK(s(cons(length(and(cons(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(cons(y0, y1), y2)), y3))) MARK(s(cons(length(and(tt, y0)), y1))) -> c14(MARK(cons(length(and(tt, y0)), y1))) MARK(s(cons(length(and(s(y0), y1)), y2))) -> c14(MARK(cons(length(and(s(y0), y1)), y2))) MARK(s(cons(length(and(y0, y1)), y2))) -> c14(MARK(cons(length(and(y0, y1)), y2))) MARK(s(cons(length(and(zeros, y0)), y1))) -> c14(MARK(cons(length(and(zeros, y0)), y1))) MARK(s(cons(length(length(zeros)), y0))) -> c14(MARK(cons(length(length(zeros)), y0))) MARK(s(cons(length(length(and(y0, y1))), y2))) -> c14(MARK(cons(length(length(and(y0, y1))), y2))) MARK(s(cons(length(length(length(y0))), y1))) -> c14(MARK(cons(length(length(length(y0))), y1))) MARK(s(cons(length(length(cons(y0, y1))), y2))) -> c14(MARK(cons(length(length(cons(y0, y1))), y2))) MARK(s(cons(length(length(s(y0))), y1))) -> c14(MARK(cons(length(length(s(y0))), y1))) MARK(s(cons(length(length(y0)), y1))) -> c14(MARK(cons(length(length(y0)), y1))) MARK(s(cons(length(zeros), y0))) -> c14(MARK(cons(length(zeros), y0))) A__LENGTH(cons(z0, s(s(y0)))) -> c5(MARK(s(s(y0)))) A__LENGTH(cons(z0, s(and(cons(y0, y1), y2)))) -> c5(MARK(s(and(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(tt, y0)))) -> c5(MARK(s(and(tt, y0)))) A__LENGTH(cons(z0, s(and(s(y0), y1)))) -> c5(MARK(s(and(s(y0), y1)))) A__LENGTH(cons(z0, s(length(cons(y0, y1))))) -> c5(MARK(s(length(cons(y0, y1))))) A__LENGTH(cons(z0, s(length(s(y0))))) -> c5(MARK(s(length(s(y0))))) A__LENGTH(cons(z0, s(and(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(length(y0), y1), y2)))) -> c5(MARK(s(and(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(tt, y0), y1)))) -> c5(MARK(s(and(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(and(and(s(y0), y1), y2)))) -> c5(MARK(s(and(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(y0, y1), y2)))) -> c5(MARK(s(and(and(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(length(zeros), y0)))) -> c5(MARK(s(and(length(zeros), y0)))) A__LENGTH(cons(z0, s(and(length(and(y0, y1)), y2)))) -> c5(MARK(s(and(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(length(y0)), y1)))) -> c5(MARK(s(and(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(cons(y0, y1)), y2)))) -> c5(MARK(s(and(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(s(y0)), y1)))) -> c5(MARK(s(and(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(y0), y1)))) -> c5(MARK(s(and(length(y0), y1)))) A__LENGTH(cons(z0, s(and(and(zeros, y0), y1)))) -> c5(MARK(s(and(and(zeros, y0), y1)))) A__LENGTH(cons(z0, s(length(and(and(y0, y1), y2))))) -> c5(MARK(s(length(and(and(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(length(y0), y1))))) -> c5(MARK(s(length(and(length(y0), y1))))) A__LENGTH(cons(z0, s(length(and(cons(y0, y1), y2))))) -> c5(MARK(s(length(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(tt, y0))))) -> c5(MARK(s(length(and(tt, y0))))) A__LENGTH(cons(z0, s(length(and(s(y0), y1))))) -> c5(MARK(s(length(and(s(y0), y1))))) A__LENGTH(cons(z0, s(length(and(y0, y1))))) -> c5(MARK(s(length(and(y0, y1))))) A__LENGTH(cons(z0, s(length(and(zeros, y0))))) -> c5(MARK(s(length(and(zeros, y0))))) A__LENGTH(cons(z0, s(length(length(zeros))))) -> c5(MARK(s(length(length(zeros))))) A__LENGTH(cons(z0, s(length(length(and(y0, y1)))))) -> c5(MARK(s(length(length(and(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(length(y0)))))) -> c5(MARK(s(length(length(length(y0)))))) A__LENGTH(cons(z0, s(length(length(cons(y0, y1)))))) -> c5(MARK(s(length(length(cons(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(s(y0)))))) -> c5(MARK(s(length(length(s(y0)))))) A__LENGTH(cons(z0, s(length(length(y0))))) -> c5(MARK(s(length(length(y0))))) A__LENGTH(cons(z0, s(length(zeros)))) -> c5(MARK(s(length(zeros)))) A__LENGTH(cons(z0, s(cons(cons(y0, y1), y2)))) -> c5(MARK(s(cons(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(cons(s(y0), y1)))) -> c5(MARK(s(cons(s(y0), y1)))) A__LENGTH(cons(z0, s(cons(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(tt, y0), y1)))) -> c5(MARK(s(cons(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(cons(and(s(y0), y1), y2)))) -> c5(MARK(s(cons(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(length(cons(y0, y1)), y2)))) -> c5(MARK(s(cons(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(s(y0)), y1)))) -> c5(MARK(s(cons(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(cons(and(and(and(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(and(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(length(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(length(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(cons(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(tt, y0), y1), y2)))) -> c5(MARK(s(cons(and(and(tt, y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(and(s(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(s(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(zeros), y0), y1)))) -> c5(MARK(s(cons(and(length(zeros), y0), y1)))) A__LENGTH(cons(z0, s(cons(and(length(and(y0, y1)), y2), y3)))) -> c5(MARK(s(cons(and(length(and(y0, y1)), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(length(y0)), y1), y2)))) -> c5(MARK(s(cons(and(length(length(y0)), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(length(cons(y0, y1)), y2), y3)))) -> c5(MARK(s(cons(and(length(cons(y0, y1)), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(s(y0)), y1), y2)))) -> c5(MARK(s(cons(and(length(s(y0)), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(length(y0), y1), y2)))) -> c5(MARK(s(cons(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(and(zeros, y0), y1), y2)))) -> c5(MARK(s(cons(and(and(zeros, y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(length(and(and(y0, y1), y2)), y3)))) -> c5(MARK(s(cons(length(and(and(y0, y1), y2)), y3)))) A__LENGTH(cons(z0, s(cons(length(and(length(y0), y1)), y2)))) -> c5(MARK(s(cons(length(and(length(y0), y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(cons(y0, y1), y2)), y3)))) -> c5(MARK(s(cons(length(and(cons(y0, y1), y2)), y3)))) A__LENGTH(cons(z0, s(cons(length(and(tt, y0)), y1)))) -> c5(MARK(s(cons(length(and(tt, y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(and(s(y0), y1)), y2)))) -> c5(MARK(s(cons(length(and(s(y0), y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(y0, y1)), y2)))) -> c5(MARK(s(cons(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(and(zeros, y0)), y1)))) -> c5(MARK(s(cons(length(and(zeros, y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(length(zeros)), y0)))) -> c5(MARK(s(cons(length(length(zeros)), y0)))) A__LENGTH(cons(z0, s(cons(length(length(and(y0, y1))), y2)))) -> c5(MARK(s(cons(length(length(and(y0, y1))), y2)))) A__LENGTH(cons(z0, s(cons(length(length(length(y0))), y1)))) -> c5(MARK(s(cons(length(length(length(y0))), y1)))) A__LENGTH(cons(z0, s(cons(length(length(cons(y0, y1))), y2)))) -> c5(MARK(s(cons(length(length(cons(y0, y1))), y2)))) A__LENGTH(cons(z0, s(cons(length(length(s(y0))), y1)))) -> c5(MARK(s(cons(length(length(s(y0))), y1)))) A__LENGTH(cons(z0, s(cons(length(length(y0)), y1)))) -> c5(MARK(s(cons(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(cons(length(zeros), y0)))) -> c5(MARK(s(cons(length(zeros), y0)))) MARK(and(cons(cons(y0, y1), z1), z2)) -> c8(MARK(cons(cons(y0, y1), z1))) MARK(and(cons(s(y0), z1), z2)) -> 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c8(MARK(cons(length(and(cons(y0, y1), y2)), z1))) MARK(and(cons(length(and(tt, y0)), z1), z2)) -> c8(MARK(cons(length(and(tt, y0)), z1))) MARK(and(cons(length(and(s(y0), y1)), z1), z2)) -> c8(MARK(cons(length(and(s(y0), y1)), z1))) MARK(and(cons(length(and(y0, y1)), z1), z2)) -> c8(MARK(cons(length(and(y0, y1)), z1))) MARK(and(cons(length(and(zeros, y0)), z1), z2)) -> c8(MARK(cons(length(and(zeros, y0)), z1))) MARK(and(cons(length(length(zeros)), z1), z2)) -> c8(MARK(cons(length(length(zeros)), z1))) MARK(and(cons(length(length(and(y0, y1))), z1), z2)) -> c8(MARK(cons(length(length(and(y0, y1))), z1))) MARK(and(cons(length(length(length(y0))), z1), z2)) -> c8(MARK(cons(length(length(length(y0))), z1))) MARK(and(cons(length(length(cons(y0, y1))), z1), z2)) -> c8(MARK(cons(length(length(cons(y0, y1))), z1))) MARK(and(cons(length(length(s(y0))), z1), z2)) -> c8(MARK(cons(length(length(s(y0))), z1))) MARK(and(cons(length(length(y0)), z1), z2)) -> c8(MARK(cons(length(length(y0)), z1))) MARK(and(cons(length(zeros), z1), z2)) -> c8(MARK(cons(length(zeros), z1))) MARK(and(tt, cons(y0, y1))) -> c8(A__AND(tt, cons(y0, y1))) MARK(and(tt, s(y0))) -> c8(A__AND(tt, s(y0))) MARK(and(tt, and(cons(y0, y1), y2))) -> c8(A__AND(tt, and(cons(y0, y1), y2))) MARK(and(tt, and(tt, y0))) -> c8(A__AND(tt, and(tt, y0))) MARK(and(tt, and(s(y0), y1))) -> c8(A__AND(tt, and(s(y0), y1))) MARK(and(tt, length(cons(y0, y1)))) -> c8(A__AND(tt, length(cons(y0, y1)))) MARK(and(tt, length(s(y0)))) -> c8(A__AND(tt, length(s(y0)))) MARK(and(tt, and(and(and(y0, y1), y2), y3))) -> c8(A__AND(tt, and(and(and(y0, y1), y2), y3))) MARK(and(tt, and(and(length(y0), y1), y2))) -> c8(A__AND(tt, and(and(length(y0), y1), y2))) MARK(and(tt, and(and(cons(y0, y1), y2), y3))) -> c8(A__AND(tt, and(and(cons(y0, y1), y2), y3))) MARK(and(tt, and(and(tt, y0), y1))) -> c8(A__AND(tt, and(and(tt, y0), y1))) MARK(and(tt, and(and(s(y0), y1), y2))) -> c8(A__AND(tt, and(and(s(y0), y1), y2))) MARK(and(tt, and(and(y0, y1), y2))) -> c8(A__AND(tt, and(and(y0, y1), y2))) MARK(and(tt, and(length(zeros), y0))) -> c8(A__AND(tt, and(length(zeros), y0))) MARK(and(tt, and(length(and(y0, y1)), y2))) -> c8(A__AND(tt, and(length(and(y0, y1)), y2))) MARK(and(tt, and(length(length(y0)), y1))) -> c8(A__AND(tt, and(length(length(y0)), y1))) MARK(and(tt, and(length(cons(y0, y1)), y2))) -> c8(A__AND(tt, and(length(cons(y0, y1)), y2))) MARK(and(tt, and(length(s(y0)), y1))) -> c8(A__AND(tt, and(length(s(y0)), y1))) MARK(and(tt, and(length(y0), y1))) -> c8(A__AND(tt, and(length(y0), y1))) MARK(and(tt, and(and(zeros, y0), y1))) -> c8(A__AND(tt, and(and(zeros, y0), y1))) MARK(and(tt, length(and(and(y0, y1), y2)))) -> c8(A__AND(tt, length(and(and(y0, y1), y2)))) MARK(and(tt, length(and(length(y0), y1)))) -> c8(A__AND(tt, length(and(length(y0), y1)))) MARK(and(tt, length(and(cons(y0, y1), y2)))) -> c8(A__AND(tt, length(and(cons(y0, y1), y2)))) MARK(and(tt, length(and(tt, y0)))) -> c8(A__AND(tt, length(and(tt, y0)))) MARK(and(tt, length(and(s(y0), y1)))) -> c8(A__AND(tt, length(and(s(y0), y1)))) MARK(and(tt, length(and(y0, y1)))) -> c8(A__AND(tt, length(and(y0, y1)))) MARK(and(tt, length(and(zeros, y0)))) -> c8(A__AND(tt, length(and(zeros, y0)))) MARK(and(tt, length(length(zeros)))) -> c8(A__AND(tt, length(length(zeros)))) MARK(and(tt, length(length(and(y0, y1))))) -> c8(A__AND(tt, length(length(and(y0, y1))))) MARK(and(tt, length(length(length(y0))))) -> c8(A__AND(tt, length(length(length(y0))))) MARK(and(tt, length(length(cons(y0, y1))))) -> c8(A__AND(tt, length(length(cons(y0, y1))))) MARK(and(tt, length(length(s(y0))))) -> c8(A__AND(tt, length(length(s(y0))))) MARK(and(tt, length(length(y0)))) -> c8(A__AND(tt, length(length(y0)))) MARK(and(tt, length(zeros))) -> c8(A__AND(tt, length(zeros))) MARK(and(s(s(y0)), z1)) -> c8(MARK(s(s(y0)))) MARK(and(s(and(cons(y0, y1), y2)), z1)) -> c8(MARK(s(and(cons(y0, y1), y2)))) MARK(and(s(and(tt, y0)), z1)) -> c8(MARK(s(and(tt, y0)))) MARK(and(s(and(s(y0), y1)), z1)) -> c8(MARK(s(and(s(y0), y1)))) MARK(and(s(length(cons(y0, y1))), z1)) -> c8(MARK(s(length(cons(y0, y1))))) MARK(and(s(length(s(y0))), z1)) -> c8(MARK(s(length(s(y0))))) MARK(and(s(and(and(and(y0, y1), y2), y3)), z1)) -> c8(MARK(s(and(and(and(y0, y1), y2), y3)))) MARK(and(s(and(and(length(y0), y1), y2)), z1)) -> c8(MARK(s(and(and(length(y0), y1), y2)))) MARK(and(s(and(and(cons(y0, y1), y2), y3)), z1)) -> c8(MARK(s(and(and(cons(y0, y1), y2), y3)))) MARK(and(s(and(and(tt, y0), y1)), z1)) -> c8(MARK(s(and(and(tt, y0), y1)))) MARK(and(s(and(and(s(y0), y1), y2)), z1)) -> c8(MARK(s(and(and(s(y0), y1), y2)))) MARK(and(s(and(and(y0, y1), y2)), z1)) -> c8(MARK(s(and(and(y0, y1), y2)))) MARK(and(s(and(length(zeros), y0)), z1)) -> c8(MARK(s(and(length(zeros), y0)))) MARK(and(s(and(length(and(y0, y1)), y2)), z1)) -> c8(MARK(s(and(length(and(y0, y1)), y2)))) MARK(and(s(and(length(length(y0)), y1)), z1)) -> c8(MARK(s(and(length(length(y0)), y1)))) MARK(and(s(and(length(cons(y0, y1)), y2)), z1)) -> c8(MARK(s(and(length(cons(y0, y1)), y2)))) MARK(and(s(and(length(s(y0)), y1)), z1)) -> c8(MARK(s(and(length(s(y0)), y1)))) MARK(and(s(and(length(y0), y1)), z1)) -> c8(MARK(s(and(length(y0), y1)))) MARK(and(s(and(and(zeros, y0), y1)), z1)) -> c8(MARK(s(and(and(zeros, y0), y1)))) MARK(and(s(length(and(and(y0, y1), y2))), z1)) -> c8(MARK(s(length(and(and(y0, y1), y2))))) MARK(and(s(length(and(length(y0), y1))), z1)) -> c8(MARK(s(length(and(length(y0), y1))))) MARK(and(s(length(and(cons(y0, y1), y2))), z1)) -> c8(MARK(s(length(and(cons(y0, y1), y2))))) MARK(and(s(length(and(tt, y0))), z1)) -> c8(MARK(s(length(and(tt, y0))))) MARK(and(s(length(and(s(y0), y1))), z1)) -> c8(MARK(s(length(and(s(y0), y1))))) MARK(and(s(length(and(y0, y1))), z1)) -> c8(MARK(s(length(and(y0, y1))))) MARK(and(s(length(and(zeros, y0))), z1)) -> c8(MARK(s(length(and(zeros, y0))))) MARK(and(s(length(length(zeros))), z1)) -> c8(MARK(s(length(length(zeros))))) MARK(and(s(length(length(and(y0, y1)))), z1)) -> c8(MARK(s(length(length(and(y0, y1)))))) MARK(and(s(length(length(length(y0)))), z1)) -> c8(MARK(s(length(length(length(y0)))))) MARK(and(s(length(length(cons(y0, y1)))), z1)) -> c8(MARK(s(length(length(cons(y0, y1)))))) MARK(and(s(length(length(s(y0)))), z1)) -> c8(MARK(s(length(length(s(y0)))))) MARK(and(s(length(length(y0))), z1)) -> c8(MARK(s(length(length(y0))))) MARK(and(s(length(zeros)), z1)) -> c8(MARK(s(length(zeros)))) MARK(and(s(cons(cons(y0, y1), y2)), z1)) -> c8(MARK(s(cons(cons(y0, y1), y2)))) MARK(and(s(cons(s(y0), y1)), z1)) -> c8(MARK(s(cons(s(y0), y1)))) MARK(and(s(cons(and(cons(y0, y1), y2), y3)), z1)) -> c8(MARK(s(cons(and(cons(y0, y1), y2), y3)))) MARK(and(s(cons(and(tt, y0), y1)), z1)) -> c8(MARK(s(cons(and(tt, y0), y1)))) MARK(and(s(cons(and(s(y0), y1), y2)), z1)) -> c8(MARK(s(cons(and(s(y0), y1), y2)))) MARK(and(s(cons(length(cons(y0, y1)), y2)), z1)) -> c8(MARK(s(cons(length(cons(y0, y1)), y2)))) MARK(and(s(cons(length(s(y0)), y1)), z1)) -> 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length(and(and(y0, y1), y2))))) A__LENGTH(cons(z0, and(tt, length(and(length(y0), y1))))) -> c5(MARK(and(tt, length(and(length(y0), y1))))) A__LENGTH(cons(z0, and(tt, length(and(cons(y0, y1), y2))))) -> c5(MARK(and(tt, length(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, and(tt, length(and(tt, y0))))) -> c5(MARK(and(tt, length(and(tt, y0))))) A__LENGTH(cons(z0, and(tt, length(and(s(y0), y1))))) -> c5(MARK(and(tt, length(and(s(y0), y1))))) A__LENGTH(cons(z0, and(tt, length(and(y0, y1))))) -> c5(MARK(and(tt, length(and(y0, y1))))) A__LENGTH(cons(z0, and(tt, length(and(zeros, y0))))) -> c5(MARK(and(tt, length(and(zeros, y0))))) A__LENGTH(cons(z0, and(tt, length(length(zeros))))) -> c5(MARK(and(tt, length(length(zeros))))) A__LENGTH(cons(z0, and(tt, length(length(and(y0, y1)))))) -> c5(MARK(and(tt, length(length(and(y0, y1)))))) A__LENGTH(cons(z0, and(tt, length(length(length(y0)))))) -> c5(MARK(and(tt, length(length(length(y0)))))) A__LENGTH(cons(z0, and(tt, length(length(cons(y0, y1)))))) -> c5(MARK(and(tt, length(length(cons(y0, y1)))))) A__LENGTH(cons(z0, and(tt, length(length(s(y0)))))) -> c5(MARK(and(tt, length(length(s(y0)))))) A__LENGTH(cons(z0, and(tt, length(length(y0))))) -> c5(MARK(and(tt, length(length(y0))))) A__LENGTH(cons(z0, and(tt, length(zeros)))) -> c5(MARK(and(tt, length(zeros)))) A__LENGTH(cons(z0, and(s(s(y0)), z2))) -> c5(MARK(and(s(s(y0)), z2))) A__LENGTH(cons(z0, and(s(and(cons(y0, y1), y2)), z2))) -> c5(MARK(and(s(and(cons(y0, y1), y2)), z2))) A__LENGTH(cons(z0, and(s(and(tt, y0)), z2))) -> c5(MARK(and(s(and(tt, y0)), z2))) A__LENGTH(cons(z0, and(s(and(s(y0), y1)), z2))) -> c5(MARK(and(s(and(s(y0), y1)), z2))) A__LENGTH(cons(z0, and(s(length(cons(y0, y1))), z2))) -> c5(MARK(and(s(length(cons(y0, y1))), z2))) A__LENGTH(cons(z0, and(s(length(s(y0))), z2))) -> c5(MARK(and(s(length(s(y0))), z2))) A__LENGTH(cons(z0, and(s(and(and(and(y0, y1), y2), y3)), z2))) -> c5(MARK(and(s(and(and(and(y0, y1), y2), y3)), z2))) A__LENGTH(cons(z0, 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c5(MARK(and(s(length(and(zeros, y0))), z2))) A__LENGTH(cons(z0, and(s(length(length(zeros))), z2))) -> c5(MARK(and(s(length(length(zeros))), z2))) A__LENGTH(cons(z0, and(s(length(length(and(y0, y1)))), z2))) -> c5(MARK(and(s(length(length(and(y0, y1)))), z2))) A__LENGTH(cons(z0, and(s(length(length(length(y0)))), z2))) -> c5(MARK(and(s(length(length(length(y0)))), z2))) A__LENGTH(cons(z0, and(s(length(length(cons(y0, y1)))), z2))) -> c5(MARK(and(s(length(length(cons(y0, y1)))), z2))) A__LENGTH(cons(z0, and(s(length(length(s(y0)))), z2))) -> c5(MARK(and(s(length(length(s(y0)))), z2))) A__LENGTH(cons(z0, and(s(length(length(y0))), z2))) -> c5(MARK(and(s(length(length(y0))), z2))) A__LENGTH(cons(z0, and(s(length(zeros)), z2))) -> c5(MARK(and(s(length(zeros)), z2))) A__LENGTH(cons(z0, and(s(cons(cons(y0, y1), y2)), z2))) -> c5(MARK(and(s(cons(cons(y0, y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(s(y0), y1)), z2))) -> c5(MARK(and(s(cons(s(y0), y1)), z2))) A__LENGTH(cons(z0, 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y1), y2)), z2))) -> c5(MARK(and(s(cons(and(and(tt, y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(s(y0), y1), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(and(s(y0), y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(y0, y1), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(and(y0, y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(zeros), y0), y1)), z2))) -> c5(MARK(and(s(cons(and(length(zeros), y0), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(and(y0, y1)), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(length(and(y0, y1)), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(length(y0)), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(length(length(y0)), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(cons(y0, y1)), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(length(cons(y0, y1)), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(s(y0)), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(length(s(y0)), y1), y2)), z2))) A__LENGTH(cons(z0, 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A__LENGTH(cons(z0, and(s(cons(length(and(zeros, y0)), y1)), z2))) -> c5(MARK(and(s(cons(length(and(zeros, y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(zeros)), y0)), z2))) -> c5(MARK(and(s(cons(length(length(zeros)), y0)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(and(y0, y1))), y2)), z2))) -> c5(MARK(and(s(cons(length(length(and(y0, y1))), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(length(y0))), y1)), z2))) -> c5(MARK(and(s(cons(length(length(length(y0))), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(cons(y0, y1))), y2)), z2))) -> c5(MARK(and(s(cons(length(length(cons(y0, y1))), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(s(y0))), y1)), z2))) -> c5(MARK(and(s(cons(length(length(s(y0))), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(length(y0)), y1)), z2))) -> c5(MARK(and(s(cons(length(length(y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(length(zeros), y0)), z2))) -> c5(MARK(and(s(cons(length(zeros), y0)), z2))) A__LENGTH(cons(z0, length(cons(y0, y1)))) -> c5(MARK(length(cons(y0, y1)))) A__LENGTH(cons(z0, length(and(and(y0, y1), y2)))) -> c5(MARK(length(and(and(y0, y1), y2)))) A__LENGTH(cons(z0, length(and(length(y0), y1)))) -> c5(MARK(length(and(length(y0), y1)))) A__LENGTH(cons(z0, length(and(cons(y0, y1), y2)))) -> c5(MARK(length(and(cons(y0, y1), y2)))) A__LENGTH(cons(z0, length(and(tt, y0)))) -> c5(MARK(length(and(tt, y0)))) A__LENGTH(cons(z0, length(and(s(y0), y1)))) -> c5(MARK(length(and(s(y0), y1)))) A__LENGTH(cons(z0, length(and(y0, y1)))) -> c5(MARK(length(and(y0, y1)))) A__LENGTH(cons(z0, length(and(zeros, y0)))) -> c5(MARK(length(and(zeros, y0)))) A__LENGTH(cons(z0, length(length(zeros)))) -> c5(MARK(length(length(zeros)))) A__LENGTH(cons(z0, length(length(and(y0, y1))))) -> c5(MARK(length(length(and(y0, y1))))) A__LENGTH(cons(z0, length(length(length(y0))))) -> c5(MARK(length(length(length(y0))))) A__LENGTH(cons(z0, length(length(cons(y0, y1))))) -> c5(MARK(length(length(cons(y0, 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c5(MARK(length(s(and(length(y0), y1))))) A__LENGTH(cons(z0, length(s(and(and(zeros, y0), y1))))) -> c5(MARK(length(s(and(and(zeros, y0), y1))))) A__LENGTH(cons(z0, length(s(length(and(and(y0, y1), y2)))))) -> c5(MARK(length(s(length(and(and(y0, y1), y2)))))) A__LENGTH(cons(z0, length(s(length(and(length(y0), y1)))))) -> c5(MARK(length(s(length(and(length(y0), y1)))))) A__LENGTH(cons(z0, length(s(length(and(cons(y0, y1), y2)))))) -> c5(MARK(length(s(length(and(cons(y0, y1), y2)))))) A__LENGTH(cons(z0, length(s(length(and(tt, y0)))))) -> c5(MARK(length(s(length(and(tt, y0)))))) A__LENGTH(cons(z0, length(s(length(and(s(y0), y1)))))) -> c5(MARK(length(s(length(and(s(y0), y1)))))) A__LENGTH(cons(z0, length(s(length(and(y0, y1)))))) -> c5(MARK(length(s(length(and(y0, y1)))))) A__LENGTH(cons(z0, length(s(length(and(zeros, y0)))))) -> c5(MARK(length(s(length(and(zeros, y0)))))) A__LENGTH(cons(z0, length(s(length(length(zeros)))))) -> c5(MARK(length(s(length(length(zeros)))))) A__LENGTH(cons(z0, length(s(length(length(and(y0, y1))))))) -> c5(MARK(length(s(length(length(and(y0, y1))))))) A__LENGTH(cons(z0, length(s(length(length(length(y0))))))) -> c5(MARK(length(s(length(length(length(y0))))))) A__LENGTH(cons(z0, length(s(length(length(cons(y0, y1))))))) -> c5(MARK(length(s(length(length(cons(y0, y1))))))) A__LENGTH(cons(z0, length(s(length(length(s(y0))))))) -> c5(MARK(length(s(length(length(s(y0))))))) A__LENGTH(cons(z0, length(s(length(length(y0)))))) -> c5(MARK(length(s(length(length(y0)))))) A__LENGTH(cons(z0, length(s(length(zeros))))) -> c5(MARK(length(s(length(zeros))))) A__LENGTH(cons(z0, length(s(cons(cons(y0, y1), y2))))) -> c5(MARK(length(s(cons(cons(y0, y1), y2))))) A__LENGTH(cons(z0, length(s(cons(s(y0), y1))))) -> c5(MARK(length(s(cons(s(y0), y1))))) A__LENGTH(cons(z0, length(s(cons(and(cons(y0, y1), y2), y3))))) -> c5(MARK(length(s(cons(and(cons(y0, y1), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(tt, y0), y1))))) -> c5(MARK(length(s(cons(and(tt, y0), y1))))) A__LENGTH(cons(z0, length(s(cons(and(s(y0), y1), y2))))) -> c5(MARK(length(s(cons(and(s(y0), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(length(cons(y0, y1)), y2))))) -> c5(MARK(length(s(cons(length(cons(y0, y1)), y2))))) A__LENGTH(cons(z0, length(s(cons(length(s(y0)), y1))))) -> c5(MARK(length(s(cons(length(s(y0)), y1))))) A__LENGTH(cons(z0, length(s(cons(and(and(and(y0, y1), y2), y3), y4))))) -> c5(MARK(length(s(cons(and(and(and(y0, y1), y2), y3), y4))))) A__LENGTH(cons(z0, length(s(cons(and(and(length(y0), y1), y2), y3))))) -> c5(MARK(length(s(cons(and(and(length(y0), y1), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(and(cons(y0, y1), y2), y3), y4))))) -> c5(MARK(length(s(cons(and(and(cons(y0, y1), y2), y3), y4))))) A__LENGTH(cons(z0, length(s(cons(and(and(tt, y0), y1), y2))))) -> c5(MARK(length(s(cons(and(and(tt, y0), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(and(and(s(y0), y1), y2), y3))))) -> c5(MARK(length(s(cons(and(and(s(y0), y1), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(and(y0, y1), y2), y3))))) -> c5(MARK(length(s(cons(and(and(y0, y1), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(length(zeros), y0), y1))))) -> c5(MARK(length(s(cons(and(length(zeros), y0), y1))))) A__LENGTH(cons(z0, length(s(cons(and(length(and(y0, y1)), y2), y3))))) -> c5(MARK(length(s(cons(and(length(and(y0, y1)), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(length(length(y0)), y1), y2))))) -> c5(MARK(length(s(cons(and(length(length(y0)), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(and(length(cons(y0, y1)), y2), y3))))) -> c5(MARK(length(s(cons(and(length(cons(y0, y1)), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(length(s(y0)), y1), y2))))) -> c5(MARK(length(s(cons(and(length(s(y0)), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(and(length(y0), y1), y2))))) -> c5(MARK(length(s(cons(and(length(y0), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(and(and(zeros, y0), y1), y2))))) -> c5(MARK(length(s(cons(and(and(zeros, y0), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(length(and(and(y0, y1), y2)), y3))))) -> c5(MARK(length(s(cons(length(and(and(y0, y1), y2)), y3))))) A__LENGTH(cons(z0, length(s(cons(length(and(length(y0), y1)), y2))))) -> c5(MARK(length(s(cons(length(and(length(y0), y1)), y2))))) A__LENGTH(cons(z0, length(s(cons(length(and(cons(y0, y1), y2)), y3))))) -> c5(MARK(length(s(cons(length(and(cons(y0, y1), y2)), y3))))) A__LENGTH(cons(z0, length(s(cons(length(and(tt, y0)), y1))))) -> c5(MARK(length(s(cons(length(and(tt, y0)), y1))))) A__LENGTH(cons(z0, length(s(cons(length(and(s(y0), y1)), y2))))) -> c5(MARK(length(s(cons(length(and(s(y0), y1)), y2))))) A__LENGTH(cons(z0, length(s(cons(length(and(y0, y1)), y2))))) -> c5(MARK(length(s(cons(length(and(y0, y1)), y2))))) A__LENGTH(cons(z0, length(s(cons(length(and(zeros, y0)), y1))))) -> c5(MARK(length(s(cons(length(and(zeros, y0)), y1))))) A__LENGTH(cons(z0, length(s(cons(length(length(zeros)), y0))))) -> c5(MARK(length(s(cons(length(length(zeros)), y0))))) A__LENGTH(cons(z0, length(s(cons(length(length(and(y0, y1))), y2))))) -> c5(MARK(length(s(cons(length(length(and(y0, y1))), y2))))) A__LENGTH(cons(z0, length(s(cons(length(length(length(y0))), y1))))) -> c5(MARK(length(s(cons(length(length(length(y0))), y1))))) A__LENGTH(cons(z0, length(s(cons(length(length(cons(y0, y1))), y2))))) -> c5(MARK(length(s(cons(length(length(cons(y0, y1))), y2))))) A__LENGTH(cons(z0, length(s(cons(length(length(s(y0))), y1))))) -> c5(MARK(length(s(cons(length(length(s(y0))), y1))))) A__LENGTH(cons(z0, length(s(cons(length(length(y0)), y1))))) -> c5(MARK(length(s(cons(length(length(y0)), y1))))) A__LENGTH(cons(z0, length(s(cons(length(zeros), y0))))) -> c5(MARK(length(s(cons(length(zeros), y0))))) MARK(and(and(and(and(y0, y1), y2), z1), z2)) -> c8(MARK(and(and(and(y0, y1), y2), z1))) MARK(and(and(and(length(y0), y1), z1), z2)) -> c8(MARK(and(and(length(y0), y1), z1))) MARK(and(and(and(cons(y0, y1), y2), z1), z2)) -> c8(MARK(and(and(cons(y0, y1), y2), z1))) MARK(and(and(and(tt, y0), z1), z2)) -> c8(MARK(and(and(tt, y0), z1))) MARK(and(and(and(s(y0), y1), z1), z2)) -> c8(MARK(and(and(s(y0), y1), z1))) MARK(and(and(and(y0, y1), z1), z2)) -> c8(MARK(and(and(y0, y1), z1))) MARK(and(and(length(zeros), z1), z2)) -> c8(MARK(and(length(zeros), z1))) MARK(and(and(length(and(y0, y1)), z1), z2)) -> c8(MARK(and(length(and(y0, y1)), z1))) MARK(and(and(length(length(y0)), z1), z2)) -> c8(MARK(and(length(length(y0)), z1))) MARK(and(and(length(cons(y0, y1)), z1), z2)) -> c8(MARK(and(length(cons(y0, y1)), z1))) MARK(and(and(length(s(y0)), z1), z2)) -> c8(MARK(and(length(s(y0)), z1))) MARK(and(and(length(y0), z1), z2)) -> c8(MARK(and(length(y0), z1))) MARK(and(and(and(zeros, y0), z1), z2)) -> c8(MARK(and(and(zeros, y0), z1))) MARK(and(and(cons(cons(y0, y1), y2), z1), z2)) -> c8(MARK(and(cons(cons(y0, y1), y2), z1))) MARK(and(and(cons(s(y0), y1), z1), z2)) -> c8(MARK(and(cons(s(y0), y1), z1))) MARK(and(and(cons(and(cons(y0, y1), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(cons(y0, y1), y2), y3), z1))) MARK(and(and(cons(and(tt, y0), y1), z1), z2)) -> c8(MARK(and(cons(and(tt, y0), y1), z1))) MARK(and(and(cons(and(s(y0), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(s(y0), y1), y2), z1))) MARK(and(and(cons(length(cons(y0, y1)), y2), z1), z2)) -> c8(MARK(and(cons(length(cons(y0, y1)), y2), z1))) MARK(and(and(cons(length(s(y0)), y1), z1), z2)) -> c8(MARK(and(cons(length(s(y0)), y1), z1))) MARK(and(and(cons(and(and(and(y0, y1), y2), y3), y4), z1), z2)) -> c8(MARK(and(cons(and(and(and(y0, y1), y2), y3), y4), z1))) MARK(and(and(cons(and(and(length(y0), y1), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(and(length(y0), y1), y2), y3), z1))) MARK(and(and(cons(and(and(cons(y0, y1), y2), y3), y4), z1), z2)) -> c8(MARK(and(cons(and(and(cons(y0, y1), y2), y3), y4), z1))) MARK(and(and(cons(and(and(tt, y0), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(and(tt, y0), y1), y2), z1))) MARK(and(and(cons(and(and(s(y0), y1), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(and(s(y0), y1), y2), y3), z1))) MARK(and(and(cons(and(and(y0, y1), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(and(y0, y1), y2), y3), z1))) MARK(and(and(cons(and(length(zeros), y0), y1), z1), z2)) -> c8(MARK(and(cons(and(length(zeros), y0), y1), z1))) MARK(and(and(cons(and(length(and(y0, y1)), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(length(and(y0, y1)), y2), y3), z1))) MARK(and(and(cons(and(length(length(y0)), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(length(length(y0)), y1), y2), z1))) MARK(and(and(cons(and(length(cons(y0, y1)), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(length(cons(y0, y1)), y2), y3), z1))) MARK(and(and(cons(and(length(s(y0)), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(length(s(y0)), y1), y2), z1))) MARK(and(and(cons(and(length(y0), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(length(y0), y1), y2), z1))) MARK(and(and(cons(and(and(zeros, y0), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(and(zeros, y0), y1), y2), z1))) MARK(and(and(cons(length(and(and(y0, y1), y2)), y3), z1), z2)) -> c8(MARK(and(cons(length(and(and(y0, y1), y2)), y3), z1))) MARK(and(and(cons(length(and(length(y0), y1)), y2), z1), z2)) -> c8(MARK(and(cons(length(and(length(y0), y1)), y2), z1))) MARK(and(and(cons(length(and(cons(y0, y1), y2)), y3), z1), z2)) -> c8(MARK(and(cons(length(and(cons(y0, y1), y2)), y3), z1))) MARK(and(and(cons(length(and(tt, y0)), y1), z1), z2)) -> c8(MARK(and(cons(length(and(tt, y0)), y1), z1))) MARK(and(and(cons(length(and(s(y0), y1)), y2), z1), z2)) -> c8(MARK(and(cons(length(and(s(y0), y1)), y2), z1))) MARK(and(and(cons(length(and(y0, y1)), y2), z1), z2)) -> c8(MARK(and(cons(length(and(y0, y1)), y2), z1))) MARK(and(and(cons(length(and(zeros, y0)), y1), z1), z2)) -> c8(MARK(and(cons(length(and(zeros, y0)), y1), z1))) MARK(and(and(cons(length(length(zeros)), y0), z1), z2)) -> c8(MARK(and(cons(length(length(zeros)), y0), z1))) MARK(and(and(cons(length(length(and(y0, y1))), y2), z1), z2)) -> c8(MARK(and(cons(length(length(and(y0, y1))), y2), z1))) MARK(and(and(cons(length(length(length(y0))), y1), z1), z2)) -> c8(MARK(and(cons(length(length(length(y0))), y1), z1))) MARK(and(and(cons(length(length(cons(y0, y1))), y2), z1), z2)) -> c8(MARK(and(cons(length(length(cons(y0, y1))), y2), z1))) MARK(and(and(cons(length(length(s(y0))), y1), z1), z2)) -> c8(MARK(and(cons(length(length(s(y0))), y1), z1))) MARK(and(and(cons(length(length(y0)), y1), z1), z2)) -> c8(MARK(and(cons(length(length(y0)), y1), z1))) MARK(and(and(cons(length(zeros), y0), z1), z2)) -> c8(MARK(and(cons(length(zeros), y0), z1))) MARK(and(and(tt, cons(y0, y1)), z2)) -> c8(MARK(and(tt, cons(y0, y1)))) MARK(and(and(tt, s(y0)), z2)) -> c8(MARK(and(tt, s(y0)))) MARK(and(and(tt, and(cons(y0, y1), y2)), z2)) -> c8(MARK(and(tt, and(cons(y0, y1), y2)))) MARK(and(and(tt, and(tt, y0)), z2)) -> c8(MARK(and(tt, and(tt, y0)))) MARK(and(and(tt, and(s(y0), y1)), z2)) -> c8(MARK(and(tt, and(s(y0), y1)))) MARK(and(and(tt, length(cons(y0, y1))), z2)) -> c8(MARK(and(tt, length(cons(y0, y1))))) MARK(and(and(tt, length(s(y0))), z2)) -> c8(MARK(and(tt, length(s(y0))))) MARK(and(and(tt, and(and(and(y0, y1), y2), y3)), z2)) -> c8(MARK(and(tt, and(and(and(y0, y1), y2), y3)))) MARK(and(and(tt, and(and(length(y0), y1), y2)), z2)) -> c8(MARK(and(tt, and(and(length(y0), y1), y2)))) MARK(and(and(tt, and(and(cons(y0, y1), y2), y3)), z2)) -> c8(MARK(and(tt, and(and(cons(y0, y1), y2), y3)))) MARK(and(and(tt, and(and(tt, y0), y1)), z2)) -> c8(MARK(and(tt, and(and(tt, y0), y1)))) MARK(and(and(tt, and(and(s(y0), y1), y2)), z2)) -> c8(MARK(and(tt, and(and(s(y0), y1), y2)))) MARK(and(and(tt, and(and(y0, y1), y2)), z2)) -> c8(MARK(and(tt, and(and(y0, y1), y2)))) MARK(and(and(tt, and(length(zeros), y0)), z2)) -> c8(MARK(and(tt, and(length(zeros), y0)))) MARK(and(and(tt, and(length(and(y0, y1)), y2)), z2)) -> c8(MARK(and(tt, and(length(and(y0, y1)), y2)))) MARK(and(and(tt, and(length(length(y0)), y1)), z2)) -> c8(MARK(and(tt, and(length(length(y0)), y1)))) MARK(and(and(tt, and(length(cons(y0, y1)), y2)), z2)) -> c8(MARK(and(tt, and(length(cons(y0, y1)), y2)))) MARK(and(and(tt, and(length(s(y0)), y1)), z2)) -> c8(MARK(and(tt, and(length(s(y0)), y1)))) MARK(and(and(tt, and(length(y0), y1)), z2)) -> c8(MARK(and(tt, and(length(y0), y1)))) MARK(and(and(tt, and(and(zeros, y0), y1)), z2)) -> c8(MARK(and(tt, and(and(zeros, y0), y1)))) MARK(and(and(tt, length(and(and(y0, y1), y2))), z2)) -> c8(MARK(and(tt, length(and(and(y0, y1), y2))))) MARK(and(and(tt, length(and(length(y0), y1))), z2)) -> c8(MARK(and(tt, length(and(length(y0), y1))))) MARK(and(and(tt, length(and(cons(y0, y1), y2))), z2)) -> c8(MARK(and(tt, length(and(cons(y0, y1), y2))))) MARK(and(and(tt, length(and(tt, y0))), z2)) -> c8(MARK(and(tt, length(and(tt, y0))))) MARK(and(and(tt, length(and(s(y0), y1))), z2)) -> c8(MARK(and(tt, length(and(s(y0), y1))))) MARK(and(and(tt, length(and(y0, y1))), z2)) -> c8(MARK(and(tt, length(and(y0, y1))))) MARK(and(and(tt, length(and(zeros, y0))), z2)) -> c8(MARK(and(tt, length(and(zeros, y0))))) MARK(and(and(tt, length(length(zeros))), z2)) -> c8(MARK(and(tt, length(length(zeros))))) MARK(and(and(tt, length(length(and(y0, y1)))), z2)) -> c8(MARK(and(tt, length(length(and(y0, y1)))))) MARK(and(and(tt, length(length(length(y0)))), z2)) -> c8(MARK(and(tt, length(length(length(y0)))))) MARK(and(and(tt, length(length(cons(y0, y1)))), z2)) -> c8(MARK(and(tt, length(length(cons(y0, y1)))))) MARK(and(and(tt, length(length(s(y0)))), z2)) -> c8(MARK(and(tt, length(length(s(y0)))))) MARK(and(and(tt, length(length(y0))), z2)) -> c8(MARK(and(tt, length(length(y0))))) MARK(and(and(tt, length(zeros)), z2)) -> c8(MARK(and(tt, length(zeros)))) MARK(and(and(s(s(y0)), z1), z2)) -> c8(MARK(and(s(s(y0)), z1))) MARK(and(and(s(and(cons(y0, y1), y2)), z1), z2)) -> c8(MARK(and(s(and(cons(y0, y1), y2)), z1))) MARK(and(and(s(and(tt, y0)), z1), z2)) -> c8(MARK(and(s(and(tt, y0)), z1))) MARK(and(and(s(and(s(y0), y1)), z1), z2)) -> c8(MARK(and(s(and(s(y0), y1)), z1))) MARK(and(and(s(length(cons(y0, y1))), z1), z2)) -> c8(MARK(and(s(length(cons(y0, y1))), z1))) MARK(and(and(s(length(s(y0))), z1), z2)) -> c8(MARK(and(s(length(s(y0))), z1))) MARK(and(and(s(and(and(and(y0, y1), y2), y3)), z1), z2)) -> c8(MARK(and(s(and(and(and(y0, y1), y2), y3)), z1))) MARK(and(and(s(and(and(length(y0), y1), y2)), z1), z2)) -> c8(MARK(and(s(and(and(length(y0), y1), y2)), z1))) MARK(and(and(s(and(and(cons(y0, y1), y2), y3)), z1), z2)) -> c8(MARK(and(s(and(and(cons(y0, y1), y2), y3)), z1))) MARK(and(and(s(and(and(tt, y0), y1)), z1), z2)) -> c8(MARK(and(s(and(and(tt, y0), y1)), z1))) MARK(and(and(s(and(and(s(y0), y1), y2)), z1), z2)) -> c8(MARK(and(s(and(and(s(y0), y1), y2)), z1))) MARK(and(and(s(and(and(y0, y1), y2)), z1), z2)) -> c8(MARK(and(s(and(and(y0, y1), y2)), z1))) MARK(and(and(s(and(length(zeros), y0)), z1), z2)) -> c8(MARK(and(s(and(length(zeros), y0)), z1))) MARK(and(and(s(and(length(and(y0, y1)), y2)), z1), z2)) -> c8(MARK(and(s(and(length(and(y0, y1)), y2)), z1))) MARK(and(and(s(and(length(length(y0)), y1)), z1), z2)) -> c8(MARK(and(s(and(length(length(y0)), y1)), z1))) MARK(and(and(s(and(length(cons(y0, y1)), y2)), z1), z2)) -> c8(MARK(and(s(and(length(cons(y0, y1)), y2)), z1))) MARK(and(and(s(and(length(s(y0)), y1)), z1), z2)) -> c8(MARK(and(s(and(length(s(y0)), y1)), z1))) MARK(and(and(s(and(length(y0), y1)), z1), z2)) -> c8(MARK(and(s(and(length(y0), y1)), z1))) MARK(and(and(s(and(and(zeros, y0), y1)), z1), z2)) -> c8(MARK(and(s(and(and(zeros, y0), y1)), z1))) MARK(and(and(s(length(and(and(y0, y1), y2))), z1), z2)) -> c8(MARK(and(s(length(and(and(y0, y1), y2))), z1))) MARK(and(and(s(length(and(length(y0), y1))), z1), z2)) -> c8(MARK(and(s(length(and(length(y0), y1))), z1))) MARK(and(and(s(length(and(cons(y0, y1), y2))), z1), z2)) -> c8(MARK(and(s(length(and(cons(y0, y1), y2))), z1))) MARK(and(and(s(length(and(tt, y0))), z1), z2)) -> c8(MARK(and(s(length(and(tt, y0))), z1))) MARK(and(and(s(length(and(s(y0), y1))), z1), z2)) -> c8(MARK(and(s(length(and(s(y0), y1))), z1))) MARK(and(and(s(length(and(y0, y1))), z1), z2)) -> c8(MARK(and(s(length(and(y0, y1))), z1))) MARK(and(and(s(length(and(zeros, y0))), z1), z2)) -> c8(MARK(and(s(length(and(zeros, y0))), z1))) MARK(and(and(s(length(length(zeros))), z1), z2)) -> c8(MARK(and(s(length(length(zeros))), z1))) MARK(and(and(s(length(length(and(y0, y1)))), z1), z2)) -> c8(MARK(and(s(length(length(and(y0, y1)))), z1))) MARK(and(and(s(length(length(length(y0)))), z1), z2)) -> c8(MARK(and(s(length(length(length(y0)))), z1))) MARK(and(and(s(length(length(cons(y0, y1)))), z1), z2)) -> c8(MARK(and(s(length(length(cons(y0, y1)))), z1))) MARK(and(and(s(length(length(s(y0)))), z1), z2)) -> c8(MARK(and(s(length(length(s(y0)))), z1))) MARK(and(and(s(length(length(y0))), z1), z2)) -> c8(MARK(and(s(length(length(y0))), z1))) MARK(and(and(s(length(zeros)), z1), z2)) -> c8(MARK(and(s(length(zeros)), z1))) MARK(and(and(s(cons(cons(y0, y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(cons(y0, y1), y2)), z1))) MARK(and(and(s(cons(s(y0), y1)), z1), z2)) -> c8(MARK(and(s(cons(s(y0), y1)), z1))) MARK(and(and(s(cons(and(cons(y0, y1), y2), y3)), z1), z2)) -> c8(MARK(and(s(cons(and(cons(y0, y1), y2), y3)), z1))) MARK(and(and(s(cons(and(tt, y0), y1)), z1), z2)) -> c8(MARK(and(s(cons(and(tt, y0), y1)), z1))) MARK(and(and(s(cons(and(s(y0), y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(and(s(y0), y1), y2)), z1))) MARK(and(and(s(cons(length(cons(y0, y1)), y2)), z1), z2)) -> c8(MARK(and(s(cons(length(cons(y0, y1)), y2)), z1))) MARK(and(and(s(cons(length(s(y0)), y1)), z1), z2)) -> c8(MARK(and(s(cons(length(s(y0)), y1)), z1))) MARK(and(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), z1), z2)) -> c8(MARK(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), z1))) MARK(and(and(s(cons(and(and(length(y0), y1), y2), y3)), z1), z2)) -> c8(MARK(and(s(cons(and(and(length(y0), y1), y2), y3)), z1))) MARK(and(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), z1), z2)) -> c8(MARK(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), z1))) MARK(and(and(s(cons(and(and(tt, y0), y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(and(and(tt, y0), y1), y2)), z1))) MARK(and(and(s(cons(and(and(s(y0), y1), y2), y3)), z1), z2)) -> c8(MARK(and(s(cons(and(and(s(y0), y1), y2), y3)), z1))) MARK(and(and(s(cons(and(and(y0, y1), y2), y3)), z1), z2)) -> c8(MARK(and(s(cons(and(and(y0, y1), y2), y3)), z1))) MARK(and(and(s(cons(and(length(zeros), y0), y1)), z1), z2)) -> c8(MARK(and(s(cons(and(length(zeros), y0), y1)), z1))) MARK(and(and(s(cons(and(length(and(y0, y1)), y2), y3)), z1), z2)) -> c8(MARK(and(s(cons(and(length(and(y0, y1)), y2), y3)), z1))) MARK(and(and(s(cons(and(length(length(y0)), y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(and(length(length(y0)), y1), y2)), z1))) MARK(and(and(s(cons(and(length(cons(y0, y1)), y2), y3)), z1), z2)) -> c8(MARK(and(s(cons(and(length(cons(y0, y1)), y2), y3)), z1))) MARK(and(and(s(cons(and(length(s(y0)), y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(and(length(s(y0)), y1), y2)), z1))) MARK(and(and(s(cons(and(length(y0), y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(and(length(y0), y1), y2)), z1))) MARK(and(and(s(cons(and(and(zeros, y0), y1), y2)), z1), z2)) -> c8(MARK(and(s(cons(and(and(zeros, y0), y1), y2)), z1))) MARK(and(and(s(cons(length(and(and(y0, y1), y2)), y3)), z1), z2)) -> c8(MARK(and(s(cons(length(and(and(y0, y1), y2)), y3)), z1))) MARK(and(and(s(cons(length(and(length(y0), y1)), y2)), z1), z2)) -> c8(MARK(and(s(cons(length(and(length(y0), y1)), y2)), z1))) MARK(and(and(s(cons(length(and(cons(y0, y1), y2)), y3)), z1), z2)) -> c8(MARK(and(s(cons(length(and(cons(y0, y1), y2)), y3)), z1))) MARK(and(and(s(cons(length(and(tt, y0)), y1)), z1), z2)) -> c8(MARK(and(s(cons(length(and(tt, y0)), y1)), z1))) MARK(and(and(s(cons(length(and(s(y0), y1)), y2)), z1), z2)) -> c8(MARK(and(s(cons(length(and(s(y0), y1)), y2)), z1))) MARK(and(and(s(cons(length(and(y0, y1)), y2)), z1), z2)) -> c8(MARK(and(s(cons(length(and(y0, y1)), y2)), z1))) MARK(and(and(s(cons(length(and(zeros, y0)), y1)), z1), z2)) -> c8(MARK(and(s(cons(length(and(zeros, y0)), y1)), z1))) MARK(and(and(s(cons(length(length(zeros)), y0)), z1), z2)) -> c8(MARK(and(s(cons(length(length(zeros)), y0)), z1))) MARK(and(and(s(cons(length(length(and(y0, y1))), y2)), z1), z2)) -> c8(MARK(and(s(cons(length(length(and(y0, y1))), y2)), z1))) MARK(and(and(s(cons(length(length(length(y0))), y1)), z1), z2)) -> c8(MARK(and(s(cons(length(length(length(y0))), y1)), z1))) MARK(and(and(s(cons(length(length(cons(y0, y1))), y2)), z1), z2)) -> c8(MARK(and(s(cons(length(length(cons(y0, y1))), y2)), z1))) MARK(and(and(s(cons(length(length(s(y0))), y1)), z1), z2)) -> c8(MARK(and(s(cons(length(length(s(y0))), y1)), z1))) MARK(and(and(s(cons(length(length(y0)), y1)), z1), z2)) -> c8(MARK(and(s(cons(length(length(y0)), y1)), z1))) MARK(and(and(s(cons(length(zeros), y0)), z1), z2)) -> c8(MARK(and(s(cons(length(zeros), y0)), z1))) MARK(and(length(cons(y0, y1)), z1)) -> c8(MARK(length(cons(y0, y1)))) MARK(and(length(and(and(y0, y1), y2)), z1)) -> c8(MARK(length(and(and(y0, y1), y2)))) MARK(and(length(and(length(y0), y1)), z1)) -> c8(MARK(length(and(length(y0), y1)))) MARK(and(length(and(cons(y0, y1), y2)), z1)) -> c8(MARK(length(and(cons(y0, y1), y2)))) MARK(and(length(and(tt, y0)), z1)) -> c8(MARK(length(and(tt, y0)))) MARK(and(length(and(s(y0), y1)), z1)) -> c8(MARK(length(and(s(y0), y1)))) MARK(and(length(and(y0, y1)), z1)) -> c8(MARK(length(and(y0, y1)))) MARK(and(length(and(zeros, y0)), z1)) -> c8(MARK(length(and(zeros, y0)))) MARK(and(length(length(zeros)), z1)) -> c8(MARK(length(length(zeros)))) MARK(and(length(length(and(y0, y1))), z1)) -> c8(MARK(length(length(and(y0, y1))))) MARK(and(length(length(length(y0))), z1)) -> c8(MARK(length(length(length(y0))))) MARK(and(length(length(cons(y0, y1))), z1)) -> c8(MARK(length(length(cons(y0, y1))))) MARK(and(length(length(s(y0))), z1)) -> c8(MARK(length(length(s(y0))))) MARK(and(length(length(y0)), z1)) -> c8(MARK(length(length(y0)))) MARK(and(length(zeros), z1)) -> c8(MARK(length(zeros))) MARK(and(length(s(s(y0))), z1)) -> c8(MARK(length(s(s(y0))))) MARK(and(length(s(and(cons(y0, y1), y2))), z1)) -> c8(MARK(length(s(and(cons(y0, y1), y2))))) MARK(and(length(s(and(tt, y0))), z1)) -> c8(MARK(length(s(and(tt, y0))))) MARK(and(length(s(and(s(y0), y1))), z1)) -> c8(MARK(length(s(and(s(y0), y1))))) MARK(and(length(s(length(cons(y0, y1)))), z1)) -> c8(MARK(length(s(length(cons(y0, y1)))))) MARK(and(length(s(length(s(y0)))), z1)) -> c8(MARK(length(s(length(s(y0)))))) MARK(and(length(s(and(and(and(y0, y1), y2), y3))), z1)) -> c8(MARK(length(s(and(and(and(y0, y1), y2), y3))))) MARK(and(length(s(and(and(length(y0), y1), y2))), z1)) -> c8(MARK(length(s(and(and(length(y0), y1), y2))))) MARK(and(length(s(and(and(cons(y0, y1), y2), y3))), z1)) -> c8(MARK(length(s(and(and(cons(y0, y1), y2), y3))))) MARK(and(length(s(and(and(tt, y0), y1))), z1)) -> c8(MARK(length(s(and(and(tt, y0), y1))))) MARK(and(length(s(and(and(s(y0), y1), y2))), z1)) -> c8(MARK(length(s(and(and(s(y0), y1), y2))))) MARK(and(length(s(and(and(y0, y1), y2))), z1)) -> c8(MARK(length(s(and(and(y0, y1), y2))))) MARK(and(length(s(and(length(zeros), y0))), z1)) -> c8(MARK(length(s(and(length(zeros), y0))))) MARK(and(length(s(and(length(and(y0, y1)), y2))), z1)) -> c8(MARK(length(s(and(length(and(y0, y1)), y2))))) MARK(and(length(s(and(length(length(y0)), y1))), z1)) -> c8(MARK(length(s(and(length(length(y0)), y1))))) MARK(and(length(s(and(length(cons(y0, y1)), y2))), z1)) -> c8(MARK(length(s(and(length(cons(y0, y1)), y2))))) MARK(and(length(s(and(length(s(y0)), y1))), z1)) -> c8(MARK(length(s(and(length(s(y0)), y1))))) MARK(and(length(s(and(length(y0), y1))), z1)) -> c8(MARK(length(s(and(length(y0), y1))))) MARK(and(length(s(and(and(zeros, y0), y1))), z1)) -> c8(MARK(length(s(and(and(zeros, y0), y1))))) MARK(and(length(s(length(and(and(y0, y1), y2)))), z1)) -> c8(MARK(length(s(length(and(and(y0, y1), y2)))))) MARK(and(length(s(length(and(length(y0), y1)))), z1)) -> c8(MARK(length(s(length(and(length(y0), y1)))))) MARK(and(length(s(length(and(cons(y0, y1), y2)))), z1)) -> c8(MARK(length(s(length(and(cons(y0, y1), y2)))))) MARK(and(length(s(length(and(tt, y0)))), z1)) -> c8(MARK(length(s(length(and(tt, y0)))))) MARK(and(length(s(length(and(s(y0), y1)))), z1)) -> c8(MARK(length(s(length(and(s(y0), y1)))))) MARK(and(length(s(length(and(y0, y1)))), z1)) -> c8(MARK(length(s(length(and(y0, y1)))))) MARK(and(length(s(length(and(zeros, y0)))), z1)) -> c8(MARK(length(s(length(and(zeros, y0)))))) MARK(and(length(s(length(length(zeros)))), z1)) -> c8(MARK(length(s(length(length(zeros)))))) MARK(and(length(s(length(length(and(y0, y1))))), z1)) -> c8(MARK(length(s(length(length(and(y0, y1))))))) MARK(and(length(s(length(length(length(y0))))), z1)) -> c8(MARK(length(s(length(length(length(y0))))))) MARK(and(length(s(length(length(cons(y0, y1))))), z1)) -> c8(MARK(length(s(length(length(cons(y0, y1))))))) MARK(and(length(s(length(length(s(y0))))), z1)) -> c8(MARK(length(s(length(length(s(y0))))))) MARK(and(length(s(length(length(y0)))), z1)) -> c8(MARK(length(s(length(length(y0)))))) MARK(and(length(s(length(zeros))), z1)) -> c8(MARK(length(s(length(zeros))))) MARK(and(length(s(cons(cons(y0, y1), y2))), z1)) -> c8(MARK(length(s(cons(cons(y0, y1), y2))))) MARK(and(length(s(cons(s(y0), y1))), z1)) -> c8(MARK(length(s(cons(s(y0), y1))))) MARK(and(length(s(cons(and(cons(y0, y1), y2), y3))), z1)) -> c8(MARK(length(s(cons(and(cons(y0, y1), y2), y3))))) MARK(and(length(s(cons(and(tt, y0), y1))), z1)) -> c8(MARK(length(s(cons(and(tt, y0), y1))))) MARK(and(length(s(cons(and(s(y0), y1), y2))), z1)) -> c8(MARK(length(s(cons(and(s(y0), y1), y2))))) MARK(and(length(s(cons(length(cons(y0, y1)), y2))), z1)) -> c8(MARK(length(s(cons(length(cons(y0, y1)), y2))))) MARK(and(length(s(cons(length(s(y0)), y1))), z1)) -> c8(MARK(length(s(cons(length(s(y0)), y1))))) MARK(and(length(s(cons(and(and(and(y0, y1), y2), y3), y4))), z1)) -> c8(MARK(length(s(cons(and(and(and(y0, y1), y2), y3), y4))))) MARK(and(length(s(cons(and(and(length(y0), y1), y2), y3))), z1)) -> c8(MARK(length(s(cons(and(and(length(y0), y1), y2), y3))))) MARK(and(length(s(cons(and(and(cons(y0, y1), y2), y3), y4))), z1)) -> c8(MARK(length(s(cons(and(and(cons(y0, y1), y2), y3), y4))))) MARK(and(length(s(cons(and(and(tt, y0), y1), y2))), z1)) -> c8(MARK(length(s(cons(and(and(tt, y0), y1), y2))))) MARK(and(length(s(cons(and(and(s(y0), y1), y2), y3))), z1)) -> c8(MARK(length(s(cons(and(and(s(y0), y1), y2), y3))))) MARK(and(length(s(cons(and(and(y0, y1), y2), y3))), z1)) -> c8(MARK(length(s(cons(and(and(y0, y1), y2), y3))))) MARK(and(length(s(cons(and(length(zeros), y0), y1))), z1)) -> c8(MARK(length(s(cons(and(length(zeros), y0), y1))))) MARK(and(length(s(cons(and(length(and(y0, y1)), y2), y3))), z1)) -> c8(MARK(length(s(cons(and(length(and(y0, y1)), y2), y3))))) MARK(and(length(s(cons(and(length(length(y0)), y1), y2))), z1)) -> c8(MARK(length(s(cons(and(length(length(y0)), y1), y2))))) MARK(and(length(s(cons(and(length(cons(y0, y1)), y2), y3))), z1)) -> c8(MARK(length(s(cons(and(length(cons(y0, y1)), y2), y3))))) MARK(and(length(s(cons(and(length(s(y0)), y1), y2))), z1)) -> c8(MARK(length(s(cons(and(length(s(y0)), y1), y2))))) MARK(and(length(s(cons(and(length(y0), y1), y2))), z1)) -> c8(MARK(length(s(cons(and(length(y0), y1), y2))))) MARK(and(length(s(cons(and(and(zeros, y0), y1), y2))), z1)) -> c8(MARK(length(s(cons(and(and(zeros, y0), y1), y2))))) MARK(and(length(s(cons(length(and(and(y0, y1), y2)), y3))), z1)) -> c8(MARK(length(s(cons(length(and(and(y0, y1), y2)), y3))))) MARK(and(length(s(cons(length(and(length(y0), y1)), y2))), z1)) -> c8(MARK(length(s(cons(length(and(length(y0), y1)), y2))))) MARK(and(length(s(cons(length(and(cons(y0, y1), y2)), y3))), z1)) -> c8(MARK(length(s(cons(length(and(cons(y0, y1), y2)), y3))))) MARK(and(length(s(cons(length(and(tt, y0)), y1))), z1)) -> c8(MARK(length(s(cons(length(and(tt, y0)), y1))))) MARK(and(length(s(cons(length(and(s(y0), y1)), y2))), z1)) -> c8(MARK(length(s(cons(length(and(s(y0), y1)), y2))))) MARK(and(length(s(cons(length(and(y0, y1)), y2))), z1)) -> c8(MARK(length(s(cons(length(and(y0, y1)), y2))))) MARK(and(length(s(cons(length(and(zeros, y0)), y1))), z1)) -> c8(MARK(length(s(cons(length(and(zeros, y0)), y1))))) MARK(and(length(s(cons(length(length(zeros)), y0))), z1)) -> c8(MARK(length(s(cons(length(length(zeros)), y0))))) MARK(and(length(s(cons(length(length(and(y0, y1))), y2))), z1)) -> c8(MARK(length(s(cons(length(length(and(y0, y1))), y2))))) MARK(and(length(s(cons(length(length(length(y0))), y1))), z1)) -> c8(MARK(length(s(cons(length(length(length(y0))), y1))))) MARK(and(length(s(cons(length(length(cons(y0, y1))), y2))), z1)) -> c8(MARK(length(s(cons(length(length(cons(y0, y1))), y2))))) MARK(and(length(s(cons(length(length(s(y0))), y1))), z1)) -> c8(MARK(length(s(cons(length(length(s(y0))), y1))))) MARK(and(length(s(cons(length(length(y0)), y1))), z1)) -> c8(MARK(length(s(cons(length(length(y0)), y1))))) MARK(and(length(s(cons(length(zeros), y0))), z1)) -> c8(MARK(length(s(cons(length(zeros), y0))))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__LENGTH_1, MARK_1, A__AND_2 Compound Symbols: c5_2, c9_2, c5_1, c8_2, c8_1, c9_1, c2_1, c10_1, c14_1 ---------------------------------------- (189) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(length(and(x0, z1))) -> c9(MARK(and(x0, z1))) by MARK(length(and(and(and(y0, y1), y2), z1))) -> c9(MARK(and(and(and(y0, y1), y2), z1))) MARK(length(and(and(length(y0), y1), z1))) -> c9(MARK(and(and(length(y0), y1), z1))) MARK(length(and(and(cons(y0, y1), y2), z1))) -> c9(MARK(and(and(cons(y0, y1), y2), z1))) MARK(length(and(and(tt, y0), z1))) -> c9(MARK(and(and(tt, y0), z1))) MARK(length(and(and(s(y0), y1), z1))) -> c9(MARK(and(and(s(y0), y1), z1))) MARK(length(and(length(zeros), z1))) -> c9(MARK(and(length(zeros), z1))) MARK(length(and(length(and(y0, y1)), z1))) -> c9(MARK(and(length(and(y0, y1)), z1))) MARK(length(and(length(length(y0)), z1))) -> c9(MARK(and(length(length(y0)), z1))) MARK(length(and(length(cons(y0, y1)), z1))) -> c9(MARK(and(length(cons(y0, y1)), z1))) MARK(length(and(length(s(y0)), z1))) -> c9(MARK(and(length(s(y0)), z1))) MARK(length(and(and(zeros, y0), z1))) -> c9(MARK(and(and(zeros, y0), z1))) MARK(length(and(cons(cons(y0, y1), y2), z1))) -> c9(MARK(and(cons(cons(y0, y1), y2), z1))) MARK(length(and(cons(s(y0), y1), z1))) -> c9(MARK(and(cons(s(y0), y1), z1))) MARK(length(and(cons(and(cons(y0, y1), y2), y3), z1))) -> c9(MARK(and(cons(and(cons(y0, y1), y2), y3), z1))) MARK(length(and(cons(and(tt, y0), y1), z1))) -> c9(MARK(and(cons(and(tt, y0), y1), z1))) MARK(length(and(cons(and(s(y0), y1), y2), z1))) -> c9(MARK(and(cons(and(s(y0), y1), y2), z1))) MARK(length(and(cons(length(cons(y0, y1)), y2), z1))) -> c9(MARK(and(cons(length(cons(y0, y1)), y2), z1))) MARK(length(and(cons(length(s(y0)), y1), z1))) -> c9(MARK(and(cons(length(s(y0)), y1), z1))) MARK(length(and(cons(and(and(and(y0, y1), y2), y3), y4), z1))) -> c9(MARK(and(cons(and(and(and(y0, y1), y2), y3), y4), z1))) MARK(length(and(cons(and(and(length(y0), y1), y2), y3), z1))) -> c9(MARK(and(cons(and(and(length(y0), y1), y2), y3), z1))) MARK(length(and(cons(and(and(cons(y0, y1), y2), y3), y4), z1))) -> c9(MARK(and(cons(and(and(cons(y0, y1), y2), y3), y4), z1))) MARK(length(and(cons(and(and(tt, y0), y1), y2), z1))) -> c9(MARK(and(cons(and(and(tt, y0), y1), y2), z1))) MARK(length(and(cons(and(and(s(y0), y1), y2), y3), z1))) -> c9(MARK(and(cons(and(and(s(y0), y1), y2), y3), z1))) MARK(length(and(cons(and(and(y0, y1), y2), y3), z1))) -> c9(MARK(and(cons(and(and(y0, y1), y2), y3), z1))) MARK(length(and(cons(and(length(zeros), y0), y1), z1))) -> c9(MARK(and(cons(and(length(zeros), y0), y1), z1))) MARK(length(and(cons(and(length(and(y0, y1)), y2), y3), z1))) -> c9(MARK(and(cons(and(length(and(y0, y1)), y2), y3), z1))) MARK(length(and(cons(and(length(length(y0)), y1), y2), z1))) -> c9(MARK(and(cons(and(length(length(y0)), y1), y2), z1))) MARK(length(and(cons(and(length(cons(y0, y1)), y2), y3), z1))) -> c9(MARK(and(cons(and(length(cons(y0, y1)), y2), y3), z1))) MARK(length(and(cons(and(length(s(y0)), y1), y2), z1))) -> c9(MARK(and(cons(and(length(s(y0)), y1), y2), z1))) MARK(length(and(cons(and(length(y0), y1), y2), z1))) -> c9(MARK(and(cons(and(length(y0), y1), y2), z1))) MARK(length(and(cons(and(and(zeros, y0), y1), y2), z1))) -> c9(MARK(and(cons(and(and(zeros, y0), y1), y2), z1))) MARK(length(and(cons(length(and(and(y0, y1), y2)), y3), z1))) -> c9(MARK(and(cons(length(and(and(y0, y1), y2)), y3), z1))) MARK(length(and(cons(length(and(length(y0), y1)), y2), z1))) -> c9(MARK(and(cons(length(and(length(y0), y1)), y2), z1))) MARK(length(and(cons(length(and(cons(y0, y1), y2)), y3), z1))) -> c9(MARK(and(cons(length(and(cons(y0, y1), y2)), y3), z1))) MARK(length(and(cons(length(and(tt, y0)), y1), z1))) -> c9(MARK(and(cons(length(and(tt, y0)), y1), z1))) MARK(length(and(cons(length(and(s(y0), y1)), y2), z1))) -> c9(MARK(and(cons(length(and(s(y0), y1)), y2), z1))) MARK(length(and(cons(length(and(y0, y1)), y2), z1))) -> c9(MARK(and(cons(length(and(y0, y1)), y2), z1))) MARK(length(and(cons(length(and(zeros, y0)), y1), z1))) -> c9(MARK(and(cons(length(and(zeros, y0)), y1), z1))) MARK(length(and(cons(length(length(zeros)), y0), z1))) -> c9(MARK(and(cons(length(length(zeros)), y0), z1))) MARK(length(and(cons(length(length(and(y0, y1))), y2), z1))) -> c9(MARK(and(cons(length(length(and(y0, y1))), y2), z1))) MARK(length(and(cons(length(length(length(y0))), y1), z1))) -> c9(MARK(and(cons(length(length(length(y0))), y1), z1))) MARK(length(and(cons(length(length(cons(y0, y1))), y2), z1))) -> c9(MARK(and(cons(length(length(cons(y0, y1))), y2), z1))) MARK(length(and(cons(length(length(s(y0))), y1), z1))) -> c9(MARK(and(cons(length(length(s(y0))), y1), z1))) MARK(length(and(cons(length(length(y0)), y1), z1))) -> c9(MARK(and(cons(length(length(y0)), y1), z1))) MARK(length(and(cons(length(zeros), y0), z1))) -> c9(MARK(and(cons(length(zeros), y0), z1))) MARK(length(and(tt, cons(y0, y1)))) -> c9(MARK(and(tt, cons(y0, y1)))) MARK(length(and(tt, s(y0)))) -> c9(MARK(and(tt, s(y0)))) MARK(length(and(tt, and(cons(y0, y1), y2)))) -> c9(MARK(and(tt, and(cons(y0, y1), y2)))) MARK(length(and(tt, and(tt, y0)))) -> c9(MARK(and(tt, and(tt, y0)))) MARK(length(and(tt, and(s(y0), y1)))) -> c9(MARK(and(tt, and(s(y0), y1)))) MARK(length(and(tt, length(cons(y0, y1))))) -> c9(MARK(and(tt, length(cons(y0, y1))))) MARK(length(and(tt, length(s(y0))))) -> c9(MARK(and(tt, length(s(y0))))) MARK(length(and(tt, and(and(and(y0, y1), y2), y3)))) -> c9(MARK(and(tt, and(and(and(y0, y1), y2), y3)))) MARK(length(and(tt, and(and(length(y0), y1), y2)))) -> c9(MARK(and(tt, and(and(length(y0), y1), y2)))) MARK(length(and(tt, and(and(cons(y0, y1), y2), y3)))) -> c9(MARK(and(tt, and(and(cons(y0, y1), y2), y3)))) MARK(length(and(tt, and(and(tt, y0), y1)))) -> c9(MARK(and(tt, and(and(tt, y0), y1)))) MARK(length(and(tt, and(and(s(y0), y1), y2)))) -> c9(MARK(and(tt, and(and(s(y0), y1), y2)))) MARK(length(and(tt, and(and(y0, y1), y2)))) -> c9(MARK(and(tt, and(and(y0, y1), y2)))) MARK(length(and(tt, and(length(zeros), y0)))) -> c9(MARK(and(tt, and(length(zeros), y0)))) MARK(length(and(tt, and(length(and(y0, y1)), y2)))) -> c9(MARK(and(tt, and(length(and(y0, y1)), y2)))) MARK(length(and(tt, and(length(length(y0)), y1)))) -> c9(MARK(and(tt, and(length(length(y0)), y1)))) MARK(length(and(tt, and(length(cons(y0, y1)), y2)))) -> c9(MARK(and(tt, and(length(cons(y0, y1)), y2)))) MARK(length(and(tt, and(length(s(y0)), y1)))) -> c9(MARK(and(tt, and(length(s(y0)), y1)))) MARK(length(and(tt, and(length(y0), y1)))) -> c9(MARK(and(tt, and(length(y0), y1)))) MARK(length(and(tt, and(and(zeros, y0), y1)))) -> c9(MARK(and(tt, and(and(zeros, y0), y1)))) MARK(length(and(tt, length(and(and(y0, y1), y2))))) -> c9(MARK(and(tt, length(and(and(y0, y1), y2))))) MARK(length(and(tt, length(and(length(y0), y1))))) -> c9(MARK(and(tt, length(and(length(y0), y1))))) MARK(length(and(tt, length(and(cons(y0, y1), y2))))) -> c9(MARK(and(tt, length(and(cons(y0, y1), y2))))) MARK(length(and(tt, length(and(tt, y0))))) -> c9(MARK(and(tt, length(and(tt, y0))))) MARK(length(and(tt, length(and(s(y0), y1))))) -> c9(MARK(and(tt, length(and(s(y0), y1))))) MARK(length(and(tt, length(and(y0, y1))))) -> c9(MARK(and(tt, length(and(y0, y1))))) MARK(length(and(tt, length(and(zeros, y0))))) -> c9(MARK(and(tt, length(and(zeros, y0))))) MARK(length(and(tt, length(length(zeros))))) -> c9(MARK(and(tt, length(length(zeros))))) MARK(length(and(tt, length(length(and(y0, y1)))))) -> c9(MARK(and(tt, length(length(and(y0, y1)))))) MARK(length(and(tt, length(length(length(y0)))))) -> c9(MARK(and(tt, length(length(length(y0)))))) MARK(length(and(tt, length(length(cons(y0, y1)))))) -> c9(MARK(and(tt, length(length(cons(y0, y1)))))) MARK(length(and(tt, length(length(s(y0)))))) -> c9(MARK(and(tt, length(length(s(y0)))))) MARK(length(and(tt, length(length(y0))))) -> c9(MARK(and(tt, length(length(y0))))) MARK(length(and(tt, length(zeros)))) -> c9(MARK(and(tt, length(zeros)))) MARK(length(and(s(s(y0)), z1))) -> c9(MARK(and(s(s(y0)), z1))) MARK(length(and(s(and(cons(y0, y1), y2)), z1))) -> c9(MARK(and(s(and(cons(y0, y1), y2)), z1))) MARK(length(and(s(and(tt, y0)), z1))) -> c9(MARK(and(s(and(tt, y0)), z1))) MARK(length(and(s(and(s(y0), y1)), z1))) -> c9(MARK(and(s(and(s(y0), y1)), z1))) MARK(length(and(s(length(cons(y0, y1))), z1))) -> c9(MARK(and(s(length(cons(y0, y1))), z1))) MARK(length(and(s(length(s(y0))), z1))) -> c9(MARK(and(s(length(s(y0))), z1))) MARK(length(and(s(and(and(and(y0, y1), y2), y3)), z1))) -> c9(MARK(and(s(and(and(and(y0, y1), y2), y3)), z1))) MARK(length(and(s(and(and(length(y0), y1), y2)), z1))) -> c9(MARK(and(s(and(and(length(y0), y1), y2)), z1))) MARK(length(and(s(and(and(cons(y0, y1), y2), y3)), z1))) -> c9(MARK(and(s(and(and(cons(y0, y1), y2), y3)), z1))) MARK(length(and(s(and(and(tt, y0), y1)), z1))) -> c9(MARK(and(s(and(and(tt, y0), y1)), z1))) MARK(length(and(s(and(and(s(y0), y1), y2)), z1))) -> c9(MARK(and(s(and(and(s(y0), y1), y2)), z1))) MARK(length(and(s(and(and(y0, y1), y2)), z1))) -> c9(MARK(and(s(and(and(y0, y1), y2)), z1))) MARK(length(and(s(and(length(zeros), y0)), z1))) -> c9(MARK(and(s(and(length(zeros), y0)), z1))) MARK(length(and(s(and(length(and(y0, y1)), y2)), z1))) -> c9(MARK(and(s(and(length(and(y0, y1)), y2)), z1))) MARK(length(and(s(and(length(length(y0)), y1)), z1))) -> c9(MARK(and(s(and(length(length(y0)), y1)), z1))) MARK(length(and(s(and(length(cons(y0, y1)), y2)), z1))) -> c9(MARK(and(s(and(length(cons(y0, y1)), y2)), z1))) MARK(length(and(s(and(length(s(y0)), y1)), z1))) -> c9(MARK(and(s(and(length(s(y0)), y1)), z1))) MARK(length(and(s(and(length(y0), y1)), z1))) -> c9(MARK(and(s(and(length(y0), y1)), z1))) MARK(length(and(s(and(and(zeros, y0), y1)), z1))) -> c9(MARK(and(s(and(and(zeros, y0), y1)), z1))) MARK(length(and(s(length(and(and(y0, y1), y2))), z1))) -> c9(MARK(and(s(length(and(and(y0, y1), y2))), z1))) MARK(length(and(s(length(and(length(y0), y1))), z1))) -> c9(MARK(and(s(length(and(length(y0), y1))), z1))) MARK(length(and(s(length(and(cons(y0, y1), y2))), z1))) -> c9(MARK(and(s(length(and(cons(y0, y1), y2))), z1))) MARK(length(and(s(length(and(tt, y0))), z1))) -> c9(MARK(and(s(length(and(tt, y0))), z1))) MARK(length(and(s(length(and(s(y0), y1))), z1))) -> c9(MARK(and(s(length(and(s(y0), y1))), z1))) MARK(length(and(s(length(and(y0, y1))), z1))) -> c9(MARK(and(s(length(and(y0, y1))), z1))) MARK(length(and(s(length(and(zeros, y0))), z1))) -> c9(MARK(and(s(length(and(zeros, y0))), z1))) MARK(length(and(s(length(length(zeros))), z1))) -> c9(MARK(and(s(length(length(zeros))), z1))) MARK(length(and(s(length(length(and(y0, y1)))), z1))) -> c9(MARK(and(s(length(length(and(y0, y1)))), z1))) MARK(length(and(s(length(length(length(y0)))), z1))) -> c9(MARK(and(s(length(length(length(y0)))), z1))) MARK(length(and(s(length(length(cons(y0, y1)))), z1))) -> c9(MARK(and(s(length(length(cons(y0, y1)))), z1))) MARK(length(and(s(length(length(s(y0)))), z1))) -> c9(MARK(and(s(length(length(s(y0)))), z1))) MARK(length(and(s(length(length(y0))), z1))) -> c9(MARK(and(s(length(length(y0))), z1))) MARK(length(and(s(length(zeros)), z1))) -> c9(MARK(and(s(length(zeros)), z1))) MARK(length(and(s(cons(cons(y0, y1), y2)), z1))) -> c9(MARK(and(s(cons(cons(y0, y1), y2)), z1))) MARK(length(and(s(cons(s(y0), y1)), z1))) -> c9(MARK(and(s(cons(s(y0), y1)), z1))) MARK(length(and(s(cons(and(cons(y0, y1), y2), y3)), z1))) -> c9(MARK(and(s(cons(and(cons(y0, y1), y2), y3)), z1))) MARK(length(and(s(cons(and(tt, y0), y1)), z1))) -> c9(MARK(and(s(cons(and(tt, y0), y1)), z1))) MARK(length(and(s(cons(and(s(y0), y1), y2)), z1))) -> c9(MARK(and(s(cons(and(s(y0), y1), y2)), z1))) MARK(length(and(s(cons(length(cons(y0, y1)), y2)), z1))) -> c9(MARK(and(s(cons(length(cons(y0, y1)), y2)), z1))) MARK(length(and(s(cons(length(s(y0)), y1)), z1))) -> c9(MARK(and(s(cons(length(s(y0)), y1)), z1))) MARK(length(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), z1))) -> c9(MARK(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), z1))) MARK(length(and(s(cons(and(and(length(y0), y1), y2), y3)), z1))) -> c9(MARK(and(s(cons(and(and(length(y0), y1), y2), y3)), z1))) MARK(length(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), z1))) -> c9(MARK(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), z1))) MARK(length(and(s(cons(and(and(tt, y0), y1), y2)), z1))) -> c9(MARK(and(s(cons(and(and(tt, y0), y1), y2)), z1))) MARK(length(and(s(cons(and(and(s(y0), y1), y2), y3)), z1))) -> c9(MARK(and(s(cons(and(and(s(y0), y1), y2), y3)), z1))) MARK(length(and(s(cons(and(and(y0, y1), y2), y3)), z1))) -> c9(MARK(and(s(cons(and(and(y0, y1), y2), y3)), z1))) MARK(length(and(s(cons(and(length(zeros), y0), y1)), z1))) -> c9(MARK(and(s(cons(and(length(zeros), y0), y1)), z1))) MARK(length(and(s(cons(and(length(and(y0, y1)), y2), y3)), z1))) -> c9(MARK(and(s(cons(and(length(and(y0, y1)), y2), y3)), z1))) MARK(length(and(s(cons(and(length(length(y0)), y1), y2)), z1))) -> c9(MARK(and(s(cons(and(length(length(y0)), y1), y2)), z1))) MARK(length(and(s(cons(and(length(cons(y0, y1)), y2), y3)), z1))) -> c9(MARK(and(s(cons(and(length(cons(y0, y1)), y2), y3)), z1))) MARK(length(and(s(cons(and(length(s(y0)), y1), y2)), z1))) -> c9(MARK(and(s(cons(and(length(s(y0)), y1), y2)), z1))) MARK(length(and(s(cons(and(length(y0), y1), y2)), z1))) -> c9(MARK(and(s(cons(and(length(y0), 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MARK(length(and(s(cons(length(length(zeros)), y0)), z1))) -> c9(MARK(and(s(cons(length(length(zeros)), y0)), z1))) MARK(length(and(s(cons(length(length(and(y0, y1))), y2)), z1))) -> c9(MARK(and(s(cons(length(length(and(y0, y1))), y2)), z1))) MARK(length(and(s(cons(length(length(length(y0))), y1)), z1))) -> c9(MARK(and(s(cons(length(length(length(y0))), y1)), z1))) MARK(length(and(s(cons(length(length(cons(y0, y1))), y2)), z1))) -> c9(MARK(and(s(cons(length(length(cons(y0, y1))), y2)), z1))) MARK(length(and(s(cons(length(length(s(y0))), y1)), z1))) -> c9(MARK(and(s(cons(length(length(s(y0))), y1)), z1))) MARK(length(and(s(cons(length(length(y0)), y1)), z1))) -> c9(MARK(and(s(cons(length(length(y0)), y1)), z1))) MARK(length(and(s(cons(length(zeros), y0)), z1))) -> c9(MARK(and(s(cons(length(zeros), y0)), z1))) MARK(length(and(and(and(and(y0, y1), y2), y3), z1))) -> c9(MARK(and(and(and(and(y0, y1), y2), y3), z1))) MARK(length(and(and(and(length(y0), y1), y2), z1))) -> 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y1), z1))) -> c9(MARK(and(and(s(length(and(zeros, y0))), y1), z1))) MARK(length(and(and(s(length(length(zeros))), y0), z1))) -> c9(MARK(and(and(s(length(length(zeros))), y0), z1))) MARK(length(and(and(s(length(length(and(y0, y1)))), y2), z1))) -> c9(MARK(and(and(s(length(length(and(y0, y1)))), y2), z1))) MARK(length(and(and(s(length(length(length(y0)))), y1), z1))) -> c9(MARK(and(and(s(length(length(length(y0)))), y1), z1))) MARK(length(and(and(s(length(length(cons(y0, y1)))), y2), z1))) -> c9(MARK(and(and(s(length(length(cons(y0, y1)))), y2), z1))) MARK(length(and(and(s(length(length(s(y0)))), y1), z1))) -> c9(MARK(and(and(s(length(length(s(y0)))), y1), z1))) MARK(length(and(and(s(length(length(y0))), y1), z1))) -> c9(MARK(and(and(s(length(length(y0))), y1), z1))) MARK(length(and(and(s(length(zeros)), y0), z1))) -> c9(MARK(and(and(s(length(zeros)), y0), z1))) MARK(length(and(and(s(cons(cons(y0, y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(cons(y0, y1), y2)), y3), z1))) MARK(length(and(and(s(cons(s(y0), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(s(y0), y1)), y2), z1))) MARK(length(and(and(s(cons(and(cons(y0, y1), y2), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(and(cons(y0, y1), y2), y3)), y4), z1))) MARK(length(and(and(s(cons(and(tt, y0), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(and(tt, y0), y1)), y2), z1))) MARK(length(and(and(s(cons(and(s(y0), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(and(s(y0), y1), y2)), y3), z1))) MARK(length(and(and(s(cons(length(cons(y0, y1)), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(length(cons(y0, y1)), y2)), y3), z1))) MARK(length(and(and(s(cons(length(s(y0)), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(length(s(y0)), y1)), y2), z1))) MARK(length(and(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), y5), z1))) -> c9(MARK(and(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), y5), z1))) MARK(length(and(and(s(cons(and(and(length(y0), y1), y2), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(and(and(length(y0), y1), y2), y3)), y4), z1))) MARK(length(and(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), y5), z1))) -> c9(MARK(and(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), y5), z1))) MARK(length(and(and(s(cons(and(and(tt, y0), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(and(and(tt, y0), y1), y2)), y3), z1))) MARK(length(and(and(s(cons(and(and(s(y0), y1), y2), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(and(and(s(y0), y1), y2), y3)), y4), z1))) MARK(length(and(and(s(cons(and(and(y0, y1), y2), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(and(and(y0, y1), y2), y3)), y4), z1))) MARK(length(and(and(s(cons(and(length(zeros), y0), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(and(length(zeros), y0), y1)), y2), z1))) MARK(length(and(and(s(cons(and(length(and(y0, y1)), y2), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(and(length(and(y0, y1)), y2), y3)), y4), z1))) MARK(length(and(and(s(cons(and(length(length(y0)), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(and(length(length(y0)), y1), y2)), y3), z1))) MARK(length(and(and(s(cons(and(length(cons(y0, y1)), y2), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(and(length(cons(y0, y1)), y2), y3)), y4), z1))) MARK(length(and(and(s(cons(and(length(s(y0)), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(and(length(s(y0)), y1), y2)), y3), z1))) MARK(length(and(and(s(cons(and(length(y0), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(and(length(y0), y1), y2)), y3), z1))) MARK(length(and(and(s(cons(and(and(zeros, y0), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(and(and(zeros, y0), y1), y2)), y3), z1))) MARK(length(and(and(s(cons(length(and(and(y0, y1), y2)), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(length(and(and(y0, y1), y2)), y3)), y4), z1))) MARK(length(and(and(s(cons(length(and(length(y0), y1)), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(length(and(length(y0), y1)), y2)), y3), z1))) MARK(length(and(and(s(cons(length(and(cons(y0, y1), y2)), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(length(and(cons(y0, y1), y2)), y3)), y4), z1))) MARK(length(and(and(s(cons(length(and(tt, y0)), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(length(and(tt, y0)), y1)), y2), z1))) MARK(length(and(and(s(cons(length(and(s(y0), y1)), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(length(and(s(y0), y1)), y2)), y3), z1))) MARK(length(and(and(s(cons(length(and(y0, y1)), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(length(and(y0, y1)), y2)), y3), z1))) MARK(length(and(and(s(cons(length(and(zeros, y0)), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(length(and(zeros, y0)), y1)), y2), z1))) MARK(length(and(and(s(cons(length(length(zeros)), y0)), y1), z1))) -> c9(MARK(and(and(s(cons(length(length(zeros)), y0)), y1), z1))) MARK(length(and(and(s(cons(length(length(and(y0, y1))), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(length(length(and(y0, y1))), y2)), y3), z1))) MARK(length(and(and(s(cons(length(length(length(y0))), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(length(length(length(y0))), y1)), y2), z1))) MARK(length(and(and(s(cons(length(length(cons(y0, y1))), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(length(length(cons(y0, y1))), y2)), y3), z1))) MARK(length(and(and(s(cons(length(length(s(y0))), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(length(length(s(y0))), y1)), y2), z1))) MARK(length(and(and(s(cons(length(length(y0)), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(length(length(y0)), y1)), y2), z1))) MARK(length(and(and(s(cons(length(zeros), y0)), y1), z1))) -> c9(MARK(and(and(s(cons(length(zeros), y0)), y1), z1))) MARK(length(and(length(and(and(y0, y1), y2)), z1))) -> c9(MARK(and(length(and(and(y0, y1), y2)), z1))) MARK(length(and(length(and(length(y0), y1)), z1))) -> c9(MARK(and(length(and(length(y0), y1)), z1))) MARK(length(and(length(and(cons(y0, y1), y2)), z1))) -> c9(MARK(and(length(and(cons(y0, y1), y2)), z1))) MARK(length(and(length(and(tt, y0)), z1))) -> c9(MARK(and(length(and(tt, y0)), z1))) MARK(length(and(length(and(s(y0), y1)), z1))) -> c9(MARK(and(length(and(s(y0), y1)), z1))) MARK(length(and(length(and(zeros, y0)), z1))) -> c9(MARK(and(length(and(zeros, y0)), z1))) MARK(length(and(length(length(zeros)), z1))) -> c9(MARK(and(length(length(zeros)), z1))) MARK(length(and(length(length(and(y0, y1))), z1))) -> c9(MARK(and(length(length(and(y0, y1))), z1))) MARK(length(and(length(length(length(y0))), z1))) -> c9(MARK(and(length(length(length(y0))), z1))) MARK(length(and(length(length(cons(y0, y1))), z1))) -> c9(MARK(and(length(length(cons(y0, y1))), z1))) MARK(length(and(length(length(s(y0))), z1))) -> c9(MARK(and(length(length(s(y0))), z1))) MARK(length(and(length(s(s(y0))), z1))) -> c9(MARK(and(length(s(s(y0))), z1))) MARK(length(and(length(s(and(cons(y0, y1), y2))), z1))) -> c9(MARK(and(length(s(and(cons(y0, y1), y2))), z1))) MARK(length(and(length(s(and(tt, y0))), z1))) -> c9(MARK(and(length(s(and(tt, y0))), z1))) MARK(length(and(length(s(and(s(y0), y1))), z1))) -> c9(MARK(and(length(s(and(s(y0), y1))), z1))) MARK(length(and(length(s(length(cons(y0, y1)))), z1))) -> c9(MARK(and(length(s(length(cons(y0, y1)))), z1))) MARK(length(and(length(s(length(s(y0)))), z1))) -> c9(MARK(and(length(s(length(s(y0)))), z1))) MARK(length(and(length(s(and(and(and(y0, y1), y2), y3))), z1))) -> c9(MARK(and(length(s(and(and(and(y0, y1), y2), y3))), z1))) MARK(length(and(length(s(and(and(length(y0), y1), y2))), z1))) -> c9(MARK(and(length(s(and(and(length(y0), y1), y2))), z1))) MARK(length(and(length(s(and(and(cons(y0, y1), y2), y3))), z1))) -> c9(MARK(and(length(s(and(and(cons(y0, y1), y2), y3))), z1))) MARK(length(and(length(s(and(and(tt, y0), y1))), z1))) -> c9(MARK(and(length(s(and(and(tt, y0), y1))), z1))) MARK(length(and(length(s(and(and(s(y0), y1), y2))), z1))) -> c9(MARK(and(length(s(and(and(s(y0), y1), y2))), z1))) MARK(length(and(length(s(and(and(y0, y1), y2))), z1))) -> c9(MARK(and(length(s(and(and(y0, y1), y2))), z1))) MARK(length(and(length(s(and(length(zeros), y0))), z1))) -> c9(MARK(and(length(s(and(length(zeros), y0))), z1))) MARK(length(and(length(s(and(length(and(y0, y1)), y2))), z1))) -> c9(MARK(and(length(s(and(length(and(y0, y1)), y2))), z1))) MARK(length(and(length(s(and(length(length(y0)), y1))), z1))) -> c9(MARK(and(length(s(and(length(length(y0)), y1))), z1))) MARK(length(and(length(s(and(length(cons(y0, y1)), y2))), z1))) -> c9(MARK(and(length(s(and(length(cons(y0, y1)), y2))), z1))) MARK(length(and(length(s(and(length(s(y0)), y1))), z1))) -> c9(MARK(and(length(s(and(length(s(y0)), y1))), z1))) MARK(length(and(length(s(and(length(y0), y1))), z1))) -> c9(MARK(and(length(s(and(length(y0), y1))), z1))) MARK(length(and(length(s(and(and(zeros, y0), y1))), z1))) -> c9(MARK(and(length(s(and(and(zeros, y0), y1))), z1))) MARK(length(and(length(s(length(and(and(y0, y1), y2)))), z1))) -> c9(MARK(and(length(s(length(and(and(y0, y1), y2)))), z1))) MARK(length(and(length(s(length(and(length(y0), y1)))), z1))) -> c9(MARK(and(length(s(length(and(length(y0), y1)))), z1))) MARK(length(and(length(s(length(and(cons(y0, y1), y2)))), z1))) -> c9(MARK(and(length(s(length(and(cons(y0, y1), y2)))), z1))) MARK(length(and(length(s(length(and(tt, y0)))), z1))) -> c9(MARK(and(length(s(length(and(tt, y0)))), z1))) MARK(length(and(length(s(length(and(s(y0), y1)))), z1))) -> c9(MARK(and(length(s(length(and(s(y0), y1)))), z1))) MARK(length(and(length(s(length(and(y0, y1)))), z1))) -> c9(MARK(and(length(s(length(and(y0, y1)))), z1))) MARK(length(and(length(s(length(and(zeros, y0)))), z1))) -> c9(MARK(and(length(s(length(and(zeros, y0)))), z1))) MARK(length(and(length(s(length(length(zeros)))), z1))) -> c9(MARK(and(length(s(length(length(zeros)))), z1))) MARK(length(and(length(s(length(length(and(y0, y1))))), z1))) -> c9(MARK(and(length(s(length(length(and(y0, y1))))), z1))) MARK(length(and(length(s(length(length(length(y0))))), z1))) -> c9(MARK(and(length(s(length(length(length(y0))))), z1))) MARK(length(and(length(s(length(length(cons(y0, y1))))), z1))) -> c9(MARK(and(length(s(length(length(cons(y0, y1))))), z1))) MARK(length(and(length(s(length(length(s(y0))))), z1))) -> c9(MARK(and(length(s(length(length(s(y0))))), z1))) MARK(length(and(length(s(length(length(y0)))), z1))) -> c9(MARK(and(length(s(length(length(y0)))), z1))) MARK(length(and(length(s(length(zeros))), z1))) -> c9(MARK(and(length(s(length(zeros))), z1))) MARK(length(and(length(s(cons(cons(y0, y1), y2))), z1))) -> c9(MARK(and(length(s(cons(cons(y0, y1), y2))), z1))) MARK(length(and(length(s(cons(s(y0), y1))), z1))) -> c9(MARK(and(length(s(cons(s(y0), y1))), z1))) MARK(length(and(length(s(cons(and(cons(y0, y1), y2), y3))), z1))) -> c9(MARK(and(length(s(cons(and(cons(y0, y1), y2), y3))), z1))) MARK(length(and(length(s(cons(and(tt, y0), y1))), z1))) -> c9(MARK(and(length(s(cons(and(tt, y0), y1))), z1))) MARK(length(and(length(s(cons(and(s(y0), y1), y2))), z1))) -> c9(MARK(and(length(s(cons(and(s(y0), y1), y2))), z1))) MARK(length(and(length(s(cons(length(cons(y0, y1)), y2))), z1))) -> c9(MARK(and(length(s(cons(length(cons(y0, y1)), y2))), z1))) MARK(length(and(length(s(cons(length(s(y0)), y1))), z1))) -> c9(MARK(and(length(s(cons(length(s(y0)), y1))), z1))) MARK(length(and(length(s(cons(and(and(and(y0, y1), y2), y3), y4))), z1))) -> c9(MARK(and(length(s(cons(and(and(and(y0, y1), y2), y3), y4))), z1))) MARK(length(and(length(s(cons(and(and(length(y0), y1), y2), y3))), z1))) -> c9(MARK(and(length(s(cons(and(and(length(y0), y1), y2), y3))), z1))) MARK(length(and(length(s(cons(and(and(cons(y0, y1), y2), y3), y4))), z1))) -> c9(MARK(and(length(s(cons(and(and(cons(y0, y1), y2), y3), y4))), z1))) MARK(length(and(length(s(cons(and(and(tt, y0), y1), y2))), z1))) -> c9(MARK(and(length(s(cons(and(and(tt, y0), y1), y2))), z1))) MARK(length(and(length(s(cons(and(and(s(y0), y1), y2), y3))), z1))) -> c9(MARK(and(length(s(cons(and(and(s(y0), y1), y2), y3))), z1))) MARK(length(and(length(s(cons(and(and(y0, y1), y2), y3))), z1))) -> c9(MARK(and(length(s(cons(and(and(y0, y1), y2), y3))), z1))) MARK(length(and(length(s(cons(and(length(zeros), y0), y1))), z1))) -> c9(MARK(and(length(s(cons(and(length(zeros), y0), y1))), z1))) MARK(length(and(length(s(cons(and(length(and(y0, y1)), y2), y3))), z1))) -> c9(MARK(and(length(s(cons(and(length(and(y0, y1)), y2), y3))), z1))) MARK(length(and(length(s(cons(and(length(length(y0)), y1), y2))), z1))) -> c9(MARK(and(length(s(cons(and(length(length(y0)), y1), y2))), z1))) MARK(length(and(length(s(cons(and(length(cons(y0, y1)), y2), y3))), z1))) -> c9(MARK(and(length(s(cons(and(length(cons(y0, y1)), y2), y3))), z1))) MARK(length(and(length(s(cons(and(length(s(y0)), y1), y2))), z1))) -> c9(MARK(and(length(s(cons(and(length(s(y0)), y1), y2))), z1))) MARK(length(and(length(s(cons(and(length(y0), y1), y2))), z1))) -> c9(MARK(and(length(s(cons(and(length(y0), y1), y2))), z1))) MARK(length(and(length(s(cons(and(and(zeros, y0), y1), y2))), z1))) -> c9(MARK(and(length(s(cons(and(and(zeros, y0), y1), y2))), z1))) MARK(length(and(length(s(cons(length(and(and(y0, y1), y2)), y3))), z1))) -> c9(MARK(and(length(s(cons(length(and(and(y0, y1), y2)), y3))), z1))) MARK(length(and(length(s(cons(length(and(length(y0), y1)), y2))), z1))) -> c9(MARK(and(length(s(cons(length(and(length(y0), y1)), y2))), z1))) MARK(length(and(length(s(cons(length(and(cons(y0, y1), y2)), y3))), z1))) -> c9(MARK(and(length(s(cons(length(and(cons(y0, y1), y2)), y3))), z1))) MARK(length(and(length(s(cons(length(and(tt, y0)), y1))), z1))) -> c9(MARK(and(length(s(cons(length(and(tt, y0)), y1))), z1))) MARK(length(and(length(s(cons(length(and(s(y0), y1)), y2))), z1))) -> c9(MARK(and(length(s(cons(length(and(s(y0), y1)), y2))), z1))) MARK(length(and(length(s(cons(length(and(y0, y1)), y2))), z1))) -> c9(MARK(and(length(s(cons(length(and(y0, y1)), y2))), z1))) MARK(length(and(length(s(cons(length(and(zeros, y0)), y1))), z1))) -> c9(MARK(and(length(s(cons(length(and(zeros, y0)), y1))), z1))) MARK(length(and(length(s(cons(length(length(zeros)), y0))), z1))) -> c9(MARK(and(length(s(cons(length(length(zeros)), y0))), z1))) MARK(length(and(length(s(cons(length(length(and(y0, y1))), y2))), z1))) -> c9(MARK(and(length(s(cons(length(length(and(y0, y1))), y2))), z1))) MARK(length(and(length(s(cons(length(length(length(y0))), y1))), z1))) -> c9(MARK(and(length(s(cons(length(length(length(y0))), y1))), z1))) MARK(length(and(length(s(cons(length(length(cons(y0, y1))), y2))), z1))) -> c9(MARK(and(length(s(cons(length(length(cons(y0, y1))), y2))), z1))) MARK(length(and(length(s(cons(length(length(s(y0))), y1))), z1))) -> c9(MARK(and(length(s(cons(length(length(s(y0))), y1))), z1))) MARK(length(and(length(s(cons(length(length(y0)), y1))), z1))) -> c9(MARK(and(length(s(cons(length(length(y0)), y1))), z1))) MARK(length(and(length(s(cons(length(zeros), y0))), z1))) -> c9(MARK(and(length(s(cons(length(zeros), y0))), z1))) ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c9(MARK(length(x0))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) MARK(cons(and(and(cons(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(cons(y0, y1), y2), y3))) MARK(cons(and(and(tt, y0), y1), z1)) -> c10(MARK(and(and(tt, y0), y1))) MARK(cons(and(and(s(y0), y1), y2), z1)) -> c10(MARK(and(and(s(y0), y1), y2))) MARK(cons(and(and(y0, y1), y2), z1)) -> c10(MARK(and(and(y0, y1), y2))) MARK(cons(and(length(zeros), y0), z1)) -> c10(MARK(and(length(zeros), y0))) MARK(cons(and(length(and(y0, y1)), y2), z1)) -> c10(MARK(and(length(and(y0, y1)), y2))) MARK(cons(and(length(length(y0)), y1), z1)) -> c10(MARK(and(length(length(y0)), y1))) MARK(cons(and(length(cons(y0, y1)), y2), z1)) -> c10(MARK(and(length(cons(y0, y1)), y2))) MARK(cons(and(length(s(y0)), y1), z1)) -> c10(MARK(and(length(s(y0)), y1))) MARK(cons(and(length(y0), y1), z1)) -> c10(MARK(and(length(y0), y1))) MARK(cons(and(and(zeros, y0), y1), z1)) -> c10(MARK(and(and(zeros, y0), y1))) MARK(cons(length(and(and(y0, y1), y2)), z1)) -> c10(MARK(length(and(and(y0, y1), y2)))) MARK(cons(length(and(length(y0), y1)), z1)) -> c10(MARK(length(and(length(y0), y1)))) MARK(cons(length(and(cons(y0, y1), y2)), z1)) -> c10(MARK(length(and(cons(y0, y1), y2)))) MARK(cons(length(and(tt, y0)), z1)) -> c10(MARK(length(and(tt, y0)))) MARK(cons(length(and(s(y0), y1)), z1)) -> c10(MARK(length(and(s(y0), y1)))) MARK(cons(length(and(y0, y1)), z1)) -> c10(MARK(length(and(y0, y1)))) MARK(cons(length(and(zeros, y0)), z1)) -> c10(MARK(length(and(zeros, y0)))) MARK(cons(length(length(zeros)), z1)) -> c10(MARK(length(length(zeros)))) MARK(cons(length(length(and(y0, y1))), z1)) -> c10(MARK(length(length(and(y0, y1))))) MARK(cons(length(length(length(y0))), z1)) -> c10(MARK(length(length(length(y0))))) MARK(cons(length(length(cons(y0, y1))), z1)) -> c10(MARK(length(length(cons(y0, y1))))) MARK(cons(length(length(s(y0))), z1)) -> c10(MARK(length(length(s(y0))))) MARK(cons(length(length(y0)), z1)) -> c10(MARK(length(length(y0)))) MARK(cons(length(zeros), z1)) -> c10(MARK(length(zeros))) MARK(s(s(y0))) -> c14(MARK(s(y0))) MARK(s(and(cons(y0, y1), y2))) -> c14(MARK(and(cons(y0, y1), y2))) MARK(s(and(tt, y0))) -> c14(MARK(and(tt, y0))) MARK(s(and(s(y0), y1))) -> c14(MARK(and(s(y0), y1))) MARK(s(length(cons(y0, y1)))) -> c14(MARK(length(cons(y0, y1)))) MARK(s(length(s(y0)))) -> c14(MARK(length(s(y0)))) MARK(s(and(and(and(y0, y1), y2), y3))) -> c14(MARK(and(and(and(y0, y1), y2), y3))) MARK(s(and(and(length(y0), y1), y2))) -> c14(MARK(and(and(length(y0), y1), y2))) MARK(s(and(and(cons(y0, y1), y2), y3))) -> c14(MARK(and(and(cons(y0, y1), y2), y3))) MARK(s(and(and(tt, y0), y1))) -> c14(MARK(and(and(tt, y0), y1))) MARK(s(and(and(s(y0), y1), y2))) -> c14(MARK(and(and(s(y0), y1), y2))) MARK(s(and(and(y0, y1), y2))) -> c14(MARK(and(and(y0, y1), y2))) MARK(s(and(length(zeros), y0))) -> c14(MARK(and(length(zeros), y0))) MARK(s(and(length(and(y0, y1)), y2))) -> c14(MARK(and(length(and(y0, y1)), y2))) MARK(s(and(length(length(y0)), y1))) -> c14(MARK(and(length(length(y0)), y1))) MARK(s(and(length(cons(y0, y1)), y2))) -> c14(MARK(and(length(cons(y0, y1)), y2))) MARK(s(and(length(s(y0)), y1))) -> c14(MARK(and(length(s(y0)), y1))) MARK(s(and(length(y0), y1))) -> c14(MARK(and(length(y0), y1))) MARK(s(and(and(zeros, y0), y1))) -> c14(MARK(and(and(zeros, y0), y1))) MARK(s(length(and(and(y0, y1), y2)))) -> c14(MARK(length(and(and(y0, y1), y2)))) MARK(s(length(and(length(y0), y1)))) -> c14(MARK(length(and(length(y0), y1)))) MARK(s(length(and(cons(y0, y1), y2)))) -> c14(MARK(length(and(cons(y0, y1), y2)))) MARK(s(length(and(tt, y0)))) -> c14(MARK(length(and(tt, y0)))) MARK(s(length(and(s(y0), y1)))) -> c14(MARK(length(and(s(y0), y1)))) MARK(s(length(and(y0, y1)))) -> c14(MARK(length(and(y0, y1)))) MARK(s(length(and(zeros, y0)))) -> c14(MARK(length(and(zeros, y0)))) MARK(s(length(length(zeros)))) -> c14(MARK(length(length(zeros)))) MARK(s(length(length(and(y0, y1))))) -> c14(MARK(length(length(and(y0, y1))))) MARK(s(length(length(length(y0))))) -> c14(MARK(length(length(length(y0))))) MARK(s(length(length(cons(y0, y1))))) -> c14(MARK(length(length(cons(y0, y1))))) MARK(s(length(length(s(y0))))) -> c14(MARK(length(length(s(y0))))) MARK(s(length(length(y0)))) -> c14(MARK(length(length(y0)))) MARK(s(length(zeros))) -> c14(MARK(length(zeros))) MARK(s(cons(cons(y0, y1), y2))) -> c14(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c14(MARK(cons(s(y0), y1))) MARK(s(cons(and(cons(y0, y1), y2), y3))) -> c14(MARK(cons(and(cons(y0, y1), y2), y3))) MARK(s(cons(and(tt, y0), y1))) -> c14(MARK(cons(and(tt, y0), y1))) MARK(s(cons(and(s(y0), y1), y2))) -> c14(MARK(cons(and(s(y0), y1), y2))) MARK(s(cons(length(cons(y0, y1)), y2))) -> c14(MARK(cons(length(cons(y0, y1)), y2))) MARK(s(cons(length(s(y0)), y1))) -> c14(MARK(cons(length(s(y0)), y1))) MARK(s(cons(and(and(and(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(and(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(length(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(length(y0), y1), y2), y3))) MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(cons(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(tt, y0), y1), y2))) -> c14(MARK(cons(and(and(tt, y0), y1), y2))) MARK(s(cons(and(and(s(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(s(y0), y1), y2), y3))) MARK(s(cons(and(and(y0, y1), y2), y3))) -> c14(MARK(cons(and(and(y0, y1), y2), y3))) MARK(s(cons(and(length(zeros), y0), y1))) -> c14(MARK(cons(and(length(zeros), y0), y1))) MARK(s(cons(and(length(and(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(and(y0, y1)), y2), y3))) MARK(s(cons(and(length(length(y0)), y1), y2))) -> c14(MARK(cons(and(length(length(y0)), y1), y2))) MARK(s(cons(and(length(cons(y0, y1)), y2), y3))) -> c14(MARK(cons(and(length(cons(y0, y1)), y2), y3))) MARK(s(cons(and(length(s(y0)), y1), y2))) -> c14(MARK(cons(and(length(s(y0)), y1), y2))) MARK(s(cons(and(length(y0), y1), y2))) -> c14(MARK(cons(and(length(y0), y1), y2))) MARK(s(cons(and(and(zeros, y0), y1), y2))) -> c14(MARK(cons(and(and(zeros, y0), y1), y2))) MARK(s(cons(length(and(and(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(and(y0, y1), y2)), y3))) MARK(s(cons(length(and(length(y0), y1)), y2))) -> c14(MARK(cons(length(and(length(y0), y1)), y2))) MARK(s(cons(length(and(cons(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(cons(y0, y1), y2)), y3))) MARK(s(cons(length(and(tt, y0)), y1))) -> c14(MARK(cons(length(and(tt, y0)), y1))) MARK(s(cons(length(and(s(y0), y1)), y2))) -> c14(MARK(cons(length(and(s(y0), y1)), y2))) MARK(s(cons(length(and(y0, y1)), y2))) -> c14(MARK(cons(length(and(y0, y1)), y2))) MARK(s(cons(length(and(zeros, y0)), y1))) -> c14(MARK(cons(length(and(zeros, y0)), y1))) MARK(s(cons(length(length(zeros)), y0))) -> c14(MARK(cons(length(length(zeros)), y0))) MARK(s(cons(length(length(and(y0, y1))), y2))) -> c14(MARK(cons(length(length(and(y0, y1))), y2))) MARK(s(cons(length(length(length(y0))), y1))) -> c14(MARK(cons(length(length(length(y0))), y1))) MARK(s(cons(length(length(cons(y0, y1))), y2))) -> c14(MARK(cons(length(length(cons(y0, y1))), y2))) MARK(s(cons(length(length(s(y0))), y1))) -> c14(MARK(cons(length(length(s(y0))), y1))) MARK(s(cons(length(length(y0)), y1))) -> c14(MARK(cons(length(length(y0)), y1))) MARK(s(cons(length(zeros), y0))) -> c14(MARK(cons(length(zeros), y0))) A__LENGTH(cons(z0, s(s(y0)))) -> c5(MARK(s(s(y0)))) A__LENGTH(cons(z0, s(and(cons(y0, y1), y2)))) -> c5(MARK(s(and(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(tt, y0)))) -> c5(MARK(s(and(tt, y0)))) A__LENGTH(cons(z0, s(and(s(y0), y1)))) -> c5(MARK(s(and(s(y0), y1)))) A__LENGTH(cons(z0, s(length(cons(y0, y1))))) -> c5(MARK(s(length(cons(y0, y1))))) A__LENGTH(cons(z0, s(length(s(y0))))) -> c5(MARK(s(length(s(y0))))) A__LENGTH(cons(z0, s(and(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(length(y0), y1), y2)))) -> c5(MARK(s(and(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(and(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(and(and(tt, y0), y1)))) -> c5(MARK(s(and(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(and(and(s(y0), y1), y2)))) -> c5(MARK(s(and(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(and(and(y0, y1), y2)))) -> c5(MARK(s(and(and(y0, y1), y2)))) A__LENGTH(cons(z0, s(and(length(zeros), y0)))) -> c5(MARK(s(and(length(zeros), y0)))) A__LENGTH(cons(z0, s(and(length(and(y0, y1)), y2)))) -> c5(MARK(s(and(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(length(y0)), y1)))) -> c5(MARK(s(and(length(length(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(cons(y0, y1)), y2)))) -> c5(MARK(s(and(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(and(length(s(y0)), y1)))) -> c5(MARK(s(and(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(and(length(y0), y1)))) -> c5(MARK(s(and(length(y0), y1)))) A__LENGTH(cons(z0, s(and(and(zeros, y0), y1)))) -> c5(MARK(s(and(and(zeros, y0), y1)))) A__LENGTH(cons(z0, s(length(and(and(y0, y1), y2))))) -> c5(MARK(s(length(and(and(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(length(y0), y1))))) -> c5(MARK(s(length(and(length(y0), y1))))) A__LENGTH(cons(z0, s(length(and(cons(y0, y1), y2))))) -> c5(MARK(s(length(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(tt, y0))))) -> c5(MARK(s(length(and(tt, y0))))) A__LENGTH(cons(z0, s(length(and(s(y0), y1))))) -> c5(MARK(s(length(and(s(y0), y1))))) A__LENGTH(cons(z0, s(length(and(y0, y1))))) -> c5(MARK(s(length(and(y0, y1))))) A__LENGTH(cons(z0, s(length(and(zeros, y0))))) -> c5(MARK(s(length(and(zeros, y0))))) A__LENGTH(cons(z0, s(length(length(zeros))))) -> c5(MARK(s(length(length(zeros))))) A__LENGTH(cons(z0, s(length(length(and(y0, y1)))))) -> c5(MARK(s(length(length(and(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(length(y0)))))) -> 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MARK(and(s(cons(and(length(length(y0)), y1), y2)), z1)) -> c8(MARK(s(cons(and(length(length(y0)), y1), y2)))) MARK(and(s(cons(and(length(cons(y0, y1)), y2), y3)), z1)) -> c8(MARK(s(cons(and(length(cons(y0, y1)), y2), y3)))) MARK(and(s(cons(and(length(s(y0)), y1), y2)), z1)) -> c8(MARK(s(cons(and(length(s(y0)), y1), y2)))) MARK(and(s(cons(and(length(y0), y1), y2)), z1)) -> c8(MARK(s(cons(and(length(y0), y1), y2)))) MARK(and(s(cons(and(and(zeros, y0), y1), y2)), z1)) -> c8(MARK(s(cons(and(and(zeros, y0), y1), y2)))) MARK(and(s(cons(length(and(and(y0, y1), y2)), y3)), z1)) -> c8(MARK(s(cons(length(and(and(y0, y1), y2)), y3)))) MARK(and(s(cons(length(and(length(y0), y1)), y2)), z1)) -> c8(MARK(s(cons(length(and(length(y0), y1)), y2)))) MARK(and(s(cons(length(and(cons(y0, y1), y2)), y3)), z1)) -> c8(MARK(s(cons(length(and(cons(y0, y1), y2)), y3)))) MARK(and(s(cons(length(and(tt, y0)), y1)), z1)) -> c8(MARK(s(cons(length(and(tt, y0)), y1)))) MARK(and(s(cons(length(and(s(y0), y1)), y2)), z1)) -> c8(MARK(s(cons(length(and(s(y0), y1)), y2)))) MARK(and(s(cons(length(and(y0, y1)), y2)), z1)) -> c8(MARK(s(cons(length(and(y0, y1)), y2)))) MARK(and(s(cons(length(and(zeros, y0)), y1)), z1)) -> c8(MARK(s(cons(length(and(zeros, y0)), y1)))) MARK(and(s(cons(length(length(zeros)), y0)), z1)) -> c8(MARK(s(cons(length(length(zeros)), y0)))) MARK(and(s(cons(length(length(and(y0, y1))), y2)), z1)) -> c8(MARK(s(cons(length(length(and(y0, y1))), y2)))) MARK(and(s(cons(length(length(length(y0))), y1)), z1)) -> c8(MARK(s(cons(length(length(length(y0))), y1)))) MARK(and(s(cons(length(length(cons(y0, y1))), y2)), z1)) -> c8(MARK(s(cons(length(length(cons(y0, y1))), y2)))) MARK(and(s(cons(length(length(s(y0))), y1)), z1)) -> c8(MARK(s(cons(length(length(s(y0))), y1)))) MARK(and(s(cons(length(length(y0)), y1)), z1)) -> c8(MARK(s(cons(length(length(y0)), y1)))) MARK(and(s(cons(length(zeros), y0)), z1)) -> c8(MARK(s(cons(length(zeros), y0)))) MARK(length(s(s(y0)))) -> c9(MARK(s(s(y0)))) MARK(length(s(and(cons(y0, y1), y2)))) -> c9(MARK(s(and(cons(y0, y1), y2)))) MARK(length(s(and(tt, y0)))) -> c9(MARK(s(and(tt, y0)))) MARK(length(s(and(s(y0), y1)))) -> c9(MARK(s(and(s(y0), y1)))) MARK(length(s(length(cons(y0, y1))))) -> c9(MARK(s(length(cons(y0, y1))))) MARK(length(s(length(s(y0))))) -> c9(MARK(s(length(s(y0))))) MARK(length(s(and(and(and(y0, y1), y2), y3)))) -> c9(MARK(s(and(and(and(y0, y1), y2), y3)))) MARK(length(s(and(and(length(y0), y1), y2)))) -> c9(MARK(s(and(and(length(y0), y1), y2)))) MARK(length(s(and(and(cons(y0, y1), y2), y3)))) -> c9(MARK(s(and(and(cons(y0, y1), y2), y3)))) MARK(length(s(and(and(tt, y0), y1)))) -> c9(MARK(s(and(and(tt, y0), y1)))) MARK(length(s(and(and(s(y0), y1), y2)))) -> c9(MARK(s(and(and(s(y0), y1), y2)))) MARK(length(s(and(and(y0, y1), y2)))) -> c9(MARK(s(and(and(y0, y1), y2)))) MARK(length(s(and(length(zeros), y0)))) -> c9(MARK(s(and(length(zeros), y0)))) MARK(length(s(and(length(and(y0, y1)), y2)))) -> c9(MARK(s(and(length(and(y0, y1)), y2)))) MARK(length(s(and(length(length(y0)), y1)))) -> c9(MARK(s(and(length(length(y0)), y1)))) MARK(length(s(and(length(cons(y0, y1)), y2)))) -> c9(MARK(s(and(length(cons(y0, y1)), y2)))) MARK(length(s(and(length(s(y0)), y1)))) -> c9(MARK(s(and(length(s(y0)), y1)))) MARK(length(s(and(length(y0), y1)))) -> c9(MARK(s(and(length(y0), y1)))) MARK(length(s(and(and(zeros, y0), y1)))) -> c9(MARK(s(and(and(zeros, y0), y1)))) MARK(length(s(length(and(and(y0, y1), y2))))) -> c9(MARK(s(length(and(and(y0, y1), y2))))) MARK(length(s(length(and(length(y0), y1))))) -> c9(MARK(s(length(and(length(y0), y1))))) MARK(length(s(length(and(cons(y0, y1), y2))))) -> c9(MARK(s(length(and(cons(y0, y1), y2))))) MARK(length(s(length(and(tt, y0))))) -> c9(MARK(s(length(and(tt, y0))))) MARK(length(s(length(and(s(y0), y1))))) -> c9(MARK(s(length(and(s(y0), y1))))) MARK(length(s(length(and(y0, y1))))) -> c9(MARK(s(length(and(y0, y1))))) MARK(length(s(length(and(zeros, y0))))) -> c9(MARK(s(length(and(zeros, 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MARK(length(s(cons(and(length(length(y0)), y1), y2)))) -> c9(MARK(s(cons(and(length(length(y0)), y1), y2)))) MARK(length(s(cons(and(length(cons(y0, y1)), y2), y3)))) -> c9(MARK(s(cons(and(length(cons(y0, y1)), y2), y3)))) MARK(length(s(cons(and(length(s(y0)), y1), y2)))) -> c9(MARK(s(cons(and(length(s(y0)), y1), y2)))) MARK(length(s(cons(and(length(y0), y1), y2)))) -> c9(MARK(s(cons(and(length(y0), y1), y2)))) MARK(length(s(cons(and(and(zeros, y0), y1), y2)))) -> c9(MARK(s(cons(and(and(zeros, y0), y1), y2)))) MARK(length(s(cons(length(and(and(y0, y1), y2)), y3)))) -> c9(MARK(s(cons(length(and(and(y0, y1), y2)), y3)))) MARK(length(s(cons(length(and(length(y0), y1)), y2)))) -> c9(MARK(s(cons(length(and(length(y0), y1)), y2)))) MARK(length(s(cons(length(and(cons(y0, y1), y2)), y3)))) -> c9(MARK(s(cons(length(and(cons(y0, y1), y2)), y3)))) MARK(length(s(cons(length(and(tt, y0)), y1)))) -> c9(MARK(s(cons(length(and(tt, y0)), y1)))) MARK(length(s(cons(length(and(s(y0), y1)), y2)))) -> c9(MARK(s(cons(length(and(s(y0), y1)), y2)))) MARK(length(s(cons(length(and(y0, y1)), y2)))) -> c9(MARK(s(cons(length(and(y0, y1)), y2)))) MARK(length(s(cons(length(and(zeros, y0)), y1)))) -> c9(MARK(s(cons(length(and(zeros, y0)), y1)))) MARK(length(s(cons(length(length(zeros)), y0)))) -> c9(MARK(s(cons(length(length(zeros)), y0)))) MARK(length(s(cons(length(length(and(y0, y1))), y2)))) -> c9(MARK(s(cons(length(length(and(y0, y1))), y2)))) MARK(length(s(cons(length(length(length(y0))), y1)))) -> c9(MARK(s(cons(length(length(length(y0))), y1)))) MARK(length(s(cons(length(length(cons(y0, y1))), y2)))) -> c9(MARK(s(cons(length(length(cons(y0, y1))), y2)))) MARK(length(s(cons(length(length(s(y0))), y1)))) -> c9(MARK(s(cons(length(length(s(y0))), y1)))) MARK(length(s(cons(length(length(y0)), y1)))) -> c9(MARK(s(cons(length(length(y0)), y1)))) MARK(length(s(cons(length(zeros), y0)))) -> c9(MARK(s(cons(length(zeros), y0)))) A__LENGTH(cons(z0, and(and(and(y0, y1), y2), z2))) -> 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c5(MARK(and(cons(and(and(length(y0), y1), y2), y3), z2))) A__LENGTH(cons(z0, and(cons(and(and(cons(y0, y1), y2), y3), y4), z2))) -> c5(MARK(and(cons(and(and(cons(y0, y1), y2), y3), y4), z2))) A__LENGTH(cons(z0, and(cons(and(and(tt, y0), y1), y2), z2))) -> c5(MARK(and(cons(and(and(tt, y0), y1), y2), z2))) A__LENGTH(cons(z0, and(cons(and(and(s(y0), y1), y2), y3), z2))) -> c5(MARK(and(cons(and(and(s(y0), y1), y2), y3), z2))) A__LENGTH(cons(z0, and(cons(and(and(y0, y1), y2), y3), z2))) -> c5(MARK(and(cons(and(and(y0, y1), y2), y3), z2))) A__LENGTH(cons(z0, and(cons(and(length(zeros), y0), y1), z2))) -> c5(MARK(and(cons(and(length(zeros), y0), y1), z2))) A__LENGTH(cons(z0, and(cons(and(length(and(y0, y1)), y2), y3), z2))) -> c5(MARK(and(cons(and(length(and(y0, y1)), y2), y3), z2))) A__LENGTH(cons(z0, and(cons(and(length(length(y0)), y1), y2), z2))) -> c5(MARK(and(cons(and(length(length(y0)), y1), y2), z2))) A__LENGTH(cons(z0, and(cons(and(length(cons(y0, y1)), y2), y3), z2))) -> c5(MARK(and(cons(and(length(cons(y0, y1)), y2), y3), z2))) A__LENGTH(cons(z0, and(cons(and(length(s(y0)), y1), y2), z2))) -> c5(MARK(and(cons(and(length(s(y0)), y1), y2), z2))) A__LENGTH(cons(z0, and(cons(and(length(y0), y1), y2), z2))) -> c5(MARK(and(cons(and(length(y0), y1), y2), z2))) A__LENGTH(cons(z0, and(cons(and(and(zeros, y0), y1), y2), z2))) -> c5(MARK(and(cons(and(and(zeros, y0), y1), y2), z2))) A__LENGTH(cons(z0, and(cons(length(and(and(y0, y1), y2)), y3), z2))) -> c5(MARK(and(cons(length(and(and(y0, y1), y2)), y3), z2))) A__LENGTH(cons(z0, and(cons(length(and(length(y0), y1)), y2), z2))) -> c5(MARK(and(cons(length(and(length(y0), y1)), y2), z2))) A__LENGTH(cons(z0, and(cons(length(and(cons(y0, y1), y2)), y3), z2))) -> c5(MARK(and(cons(length(and(cons(y0, y1), y2)), y3), z2))) A__LENGTH(cons(z0, and(cons(length(and(tt, y0)), y1), z2))) -> c5(MARK(and(cons(length(and(tt, y0)), y1), z2))) A__LENGTH(cons(z0, and(cons(length(and(s(y0), y1)), y2), z2))) -> 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c9(MARK(and(and(s(cons(and(tt, y0), y1)), y2), z1))) MARK(length(and(and(s(cons(and(s(y0), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(and(s(y0), y1), y2)), y3), z1))) MARK(length(and(and(s(cons(length(cons(y0, y1)), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(length(cons(y0, y1)), y2)), y3), z1))) MARK(length(and(and(s(cons(length(s(y0)), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(length(s(y0)), y1)), y2), z1))) MARK(length(and(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), y5), z1))) -> c9(MARK(and(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), y5), z1))) MARK(length(and(and(s(cons(and(and(length(y0), y1), y2), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(and(and(length(y0), y1), y2), y3)), y4), z1))) MARK(length(and(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), y5), z1))) -> c9(MARK(and(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), y5), z1))) MARK(length(and(and(s(cons(and(and(tt, y0), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(and(and(tt, y0), y1), y2)), y3), z1))) MARK(length(and(and(s(cons(and(and(s(y0), y1), y2), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(and(and(s(y0), y1), y2), y3)), y4), z1))) MARK(length(and(and(s(cons(and(and(y0, y1), y2), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(and(and(y0, y1), y2), y3)), y4), z1))) MARK(length(and(and(s(cons(and(length(zeros), y0), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(and(length(zeros), y0), y1)), y2), z1))) MARK(length(and(and(s(cons(and(length(and(y0, y1)), y2), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(and(length(and(y0, y1)), y2), y3)), y4), z1))) MARK(length(and(and(s(cons(and(length(length(y0)), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(and(length(length(y0)), y1), y2)), y3), z1))) MARK(length(and(and(s(cons(and(length(cons(y0, y1)), y2), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(and(length(cons(y0, y1)), y2), y3)), y4), z1))) MARK(length(and(and(s(cons(and(length(s(y0)), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(and(length(s(y0)), y1), y2)), y3), z1))) MARK(length(and(and(s(cons(and(length(y0), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(and(length(y0), y1), y2)), y3), z1))) MARK(length(and(and(s(cons(and(and(zeros, y0), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(and(and(zeros, y0), y1), y2)), y3), z1))) MARK(length(and(and(s(cons(length(and(and(y0, y1), y2)), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(length(and(and(y0, y1), y2)), y3)), y4), z1))) MARK(length(and(and(s(cons(length(and(length(y0), y1)), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(length(and(length(y0), y1)), y2)), y3), z1))) MARK(length(and(and(s(cons(length(and(cons(y0, y1), y2)), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(length(and(cons(y0, y1), y2)), y3)), y4), z1))) MARK(length(and(and(s(cons(length(and(tt, y0)), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(length(and(tt, y0)), y1)), y2), z1))) MARK(length(and(and(s(cons(length(and(s(y0), y1)), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(length(and(s(y0), y1)), y2)), y3), z1))) MARK(length(and(and(s(cons(length(and(y0, y1)), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(length(and(y0, y1)), y2)), y3), z1))) MARK(length(and(and(s(cons(length(and(zeros, y0)), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(length(and(zeros, y0)), y1)), y2), z1))) MARK(length(and(and(s(cons(length(length(zeros)), y0)), y1), z1))) -> c9(MARK(and(and(s(cons(length(length(zeros)), y0)), y1), z1))) MARK(length(and(and(s(cons(length(length(and(y0, y1))), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(length(length(and(y0, y1))), y2)), y3), z1))) MARK(length(and(and(s(cons(length(length(length(y0))), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(length(length(length(y0))), y1)), y2), z1))) MARK(length(and(and(s(cons(length(length(cons(y0, y1))), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(length(length(cons(y0, y1))), y2)), y3), z1))) MARK(length(and(and(s(cons(length(length(s(y0))), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(length(length(s(y0))), y1)), y2), z1))) MARK(length(and(and(s(cons(length(length(y0)), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(length(length(y0)), y1)), y2), z1))) MARK(length(and(and(s(cons(length(zeros), y0)), y1), z1))) -> c9(MARK(and(and(s(cons(length(zeros), y0)), y1), z1))) MARK(length(and(length(and(and(y0, y1), y2)), z1))) -> c9(MARK(and(length(and(and(y0, y1), y2)), z1))) MARK(length(and(length(and(length(y0), y1)), z1))) -> c9(MARK(and(length(and(length(y0), y1)), z1))) MARK(length(and(length(and(cons(y0, y1), y2)), z1))) -> c9(MARK(and(length(and(cons(y0, y1), y2)), z1))) MARK(length(and(length(and(tt, y0)), z1))) -> c9(MARK(and(length(and(tt, y0)), z1))) MARK(length(and(length(and(s(y0), y1)), z1))) -> c9(MARK(and(length(and(s(y0), y1)), z1))) MARK(length(and(length(and(zeros, y0)), z1))) -> c9(MARK(and(length(and(zeros, y0)), z1))) MARK(length(and(length(length(zeros)), z1))) -> c9(MARK(and(length(length(zeros)), z1))) MARK(length(and(length(length(and(y0, y1))), z1))) -> c9(MARK(and(length(length(and(y0, y1))), z1))) MARK(length(and(length(length(length(y0))), z1))) -> c9(MARK(and(length(length(length(y0))), z1))) MARK(length(and(length(length(cons(y0, y1))), z1))) -> c9(MARK(and(length(length(cons(y0, y1))), z1))) MARK(length(and(length(length(s(y0))), z1))) -> c9(MARK(and(length(length(s(y0))), z1))) MARK(length(and(length(s(s(y0))), z1))) -> c9(MARK(and(length(s(s(y0))), z1))) MARK(length(and(length(s(and(cons(y0, y1), y2))), z1))) -> c9(MARK(and(length(s(and(cons(y0, y1), y2))), z1))) MARK(length(and(length(s(and(tt, y0))), z1))) -> c9(MARK(and(length(s(and(tt, y0))), z1))) MARK(length(and(length(s(and(s(y0), y1))), z1))) -> c9(MARK(and(length(s(and(s(y0), y1))), z1))) MARK(length(and(length(s(length(cons(y0, y1)))), z1))) -> c9(MARK(and(length(s(length(cons(y0, y1)))), z1))) MARK(length(and(length(s(length(s(y0)))), z1))) -> c9(MARK(and(length(s(length(s(y0)))), z1))) MARK(length(and(length(s(and(and(and(y0, y1), y2), y3))), z1))) -> c9(MARK(and(length(s(and(and(and(y0, y1), y2), y3))), z1))) MARK(length(and(length(s(and(and(length(y0), y1), y2))), z1))) -> c9(MARK(and(length(s(and(and(length(y0), y1), y2))), z1))) MARK(length(and(length(s(and(and(cons(y0, y1), y2), y3))), z1))) -> c9(MARK(and(length(s(and(and(cons(y0, y1), y2), y3))), z1))) MARK(length(and(length(s(and(and(tt, y0), y1))), z1))) -> c9(MARK(and(length(s(and(and(tt, y0), y1))), z1))) MARK(length(and(length(s(and(and(s(y0), y1), y2))), z1))) -> c9(MARK(and(length(s(and(and(s(y0), y1), y2))), z1))) MARK(length(and(length(s(and(and(y0, y1), y2))), z1))) -> c9(MARK(and(length(s(and(and(y0, y1), y2))), z1))) MARK(length(and(length(s(and(length(zeros), y0))), z1))) -> c9(MARK(and(length(s(and(length(zeros), y0))), z1))) MARK(length(and(length(s(and(length(and(y0, y1)), y2))), z1))) -> c9(MARK(and(length(s(and(length(and(y0, y1)), y2))), z1))) MARK(length(and(length(s(and(length(length(y0)), y1))), z1))) -> c9(MARK(and(length(s(and(length(length(y0)), y1))), z1))) MARK(length(and(length(s(and(length(cons(y0, y1)), y2))), z1))) -> c9(MARK(and(length(s(and(length(cons(y0, y1)), y2))), z1))) MARK(length(and(length(s(and(length(s(y0)), y1))), z1))) -> c9(MARK(and(length(s(and(length(s(y0)), y1))), z1))) MARK(length(and(length(s(and(length(y0), y1))), z1))) -> c9(MARK(and(length(s(and(length(y0), y1))), z1))) MARK(length(and(length(s(and(and(zeros, y0), y1))), z1))) -> c9(MARK(and(length(s(and(and(zeros, y0), y1))), z1))) MARK(length(and(length(s(length(and(and(y0, y1), y2)))), z1))) -> c9(MARK(and(length(s(length(and(and(y0, y1), y2)))), z1))) MARK(length(and(length(s(length(and(length(y0), y1)))), z1))) -> c9(MARK(and(length(s(length(and(length(y0), y1)))), z1))) MARK(length(and(length(s(length(and(cons(y0, y1), y2)))), z1))) -> c9(MARK(and(length(s(length(and(cons(y0, y1), y2)))), z1))) MARK(length(and(length(s(length(and(tt, y0)))), z1))) -> c9(MARK(and(length(s(length(and(tt, y0)))), z1))) MARK(length(and(length(s(length(and(s(y0), y1)))), z1))) -> c9(MARK(and(length(s(length(and(s(y0), y1)))), z1))) MARK(length(and(length(s(length(and(y0, y1)))), z1))) -> c9(MARK(and(length(s(length(and(y0, y1)))), z1))) MARK(length(and(length(s(length(and(zeros, y0)))), z1))) -> c9(MARK(and(length(s(length(and(zeros, y0)))), z1))) MARK(length(and(length(s(length(length(zeros)))), z1))) -> c9(MARK(and(length(s(length(length(zeros)))), z1))) MARK(length(and(length(s(length(length(and(y0, y1))))), z1))) -> c9(MARK(and(length(s(length(length(and(y0, y1))))), z1))) MARK(length(and(length(s(length(length(length(y0))))), z1))) -> c9(MARK(and(length(s(length(length(length(y0))))), z1))) MARK(length(and(length(s(length(length(cons(y0, y1))))), z1))) -> c9(MARK(and(length(s(length(length(cons(y0, y1))))), z1))) MARK(length(and(length(s(length(length(s(y0))))), z1))) -> c9(MARK(and(length(s(length(length(s(y0))))), z1))) MARK(length(and(length(s(length(length(y0)))), z1))) -> c9(MARK(and(length(s(length(length(y0)))), z1))) MARK(length(and(length(s(length(zeros))), z1))) -> c9(MARK(and(length(s(length(zeros))), z1))) MARK(length(and(length(s(cons(cons(y0, y1), y2))), z1))) -> c9(MARK(and(length(s(cons(cons(y0, y1), y2))), z1))) MARK(length(and(length(s(cons(s(y0), y1))), z1))) -> c9(MARK(and(length(s(cons(s(y0), y1))), z1))) MARK(length(and(length(s(cons(and(cons(y0, y1), y2), y3))), z1))) -> c9(MARK(and(length(s(cons(and(cons(y0, y1), y2), y3))), z1))) MARK(length(and(length(s(cons(and(tt, y0), y1))), z1))) -> c9(MARK(and(length(s(cons(and(tt, y0), y1))), z1))) MARK(length(and(length(s(cons(and(s(y0), y1), y2))), z1))) -> c9(MARK(and(length(s(cons(and(s(y0), y1), y2))), z1))) MARK(length(and(length(s(cons(length(cons(y0, y1)), y2))), z1))) -> c9(MARK(and(length(s(cons(length(cons(y0, y1)), y2))), z1))) MARK(length(and(length(s(cons(length(s(y0)), y1))), z1))) -> c9(MARK(and(length(s(cons(length(s(y0)), y1))), z1))) MARK(length(and(length(s(cons(and(and(and(y0, y1), y2), y3), y4))), z1))) -> c9(MARK(and(length(s(cons(and(and(and(y0, y1), y2), y3), y4))), z1))) MARK(length(and(length(s(cons(and(and(length(y0), y1), y2), y3))), z1))) -> c9(MARK(and(length(s(cons(and(and(length(y0), y1), y2), y3))), z1))) MARK(length(and(length(s(cons(and(and(cons(y0, y1), y2), y3), y4))), z1))) -> c9(MARK(and(length(s(cons(and(and(cons(y0, y1), y2), y3), y4))), z1))) MARK(length(and(length(s(cons(and(and(tt, y0), y1), y2))), z1))) -> c9(MARK(and(length(s(cons(and(and(tt, y0), y1), y2))), z1))) MARK(length(and(length(s(cons(and(and(s(y0), y1), y2), y3))), z1))) -> c9(MARK(and(length(s(cons(and(and(s(y0), y1), y2), y3))), z1))) MARK(length(and(length(s(cons(and(and(y0, y1), y2), y3))), z1))) -> c9(MARK(and(length(s(cons(and(and(y0, y1), y2), y3))), z1))) MARK(length(and(length(s(cons(and(length(zeros), y0), y1))), z1))) -> c9(MARK(and(length(s(cons(and(length(zeros), y0), y1))), z1))) MARK(length(and(length(s(cons(and(length(and(y0, y1)), y2), y3))), z1))) -> c9(MARK(and(length(s(cons(and(length(and(y0, y1)), y2), y3))), z1))) MARK(length(and(length(s(cons(and(length(length(y0)), y1), y2))), z1))) -> c9(MARK(and(length(s(cons(and(length(length(y0)), y1), y2))), z1))) MARK(length(and(length(s(cons(and(length(cons(y0, y1)), y2), y3))), z1))) -> c9(MARK(and(length(s(cons(and(length(cons(y0, y1)), y2), y3))), z1))) MARK(length(and(length(s(cons(and(length(s(y0)), y1), y2))), z1))) -> c9(MARK(and(length(s(cons(and(length(s(y0)), y1), y2))), z1))) MARK(length(and(length(s(cons(and(length(y0), y1), y2))), z1))) -> c9(MARK(and(length(s(cons(and(length(y0), y1), y2))), z1))) MARK(length(and(length(s(cons(and(and(zeros, y0), y1), y2))), z1))) -> c9(MARK(and(length(s(cons(and(and(zeros, y0), y1), y2))), z1))) MARK(length(and(length(s(cons(length(and(and(y0, y1), y2)), y3))), z1))) -> c9(MARK(and(length(s(cons(length(and(and(y0, y1), y2)), y3))), z1))) MARK(length(and(length(s(cons(length(and(length(y0), y1)), y2))), z1))) -> c9(MARK(and(length(s(cons(length(and(length(y0), y1)), y2))), z1))) MARK(length(and(length(s(cons(length(and(cons(y0, y1), y2)), y3))), z1))) -> c9(MARK(and(length(s(cons(length(and(cons(y0, y1), y2)), y3))), z1))) MARK(length(and(length(s(cons(length(and(tt, y0)), y1))), z1))) -> c9(MARK(and(length(s(cons(length(and(tt, y0)), y1))), z1))) MARK(length(and(length(s(cons(length(and(s(y0), y1)), y2))), z1))) -> c9(MARK(and(length(s(cons(length(and(s(y0), y1)), y2))), z1))) MARK(length(and(length(s(cons(length(and(y0, y1)), y2))), z1))) -> c9(MARK(and(length(s(cons(length(and(y0, y1)), y2))), z1))) MARK(length(and(length(s(cons(length(and(zeros, y0)), y1))), z1))) -> c9(MARK(and(length(s(cons(length(and(zeros, y0)), y1))), z1))) MARK(length(and(length(s(cons(length(length(zeros)), y0))), z1))) -> c9(MARK(and(length(s(cons(length(length(zeros)), y0))), z1))) MARK(length(and(length(s(cons(length(length(and(y0, y1))), y2))), z1))) -> c9(MARK(and(length(s(cons(length(length(and(y0, y1))), y2))), z1))) MARK(length(and(length(s(cons(length(length(length(y0))), y1))), z1))) -> c9(MARK(and(length(s(cons(length(length(length(y0))), y1))), z1))) MARK(length(and(length(s(cons(length(length(cons(y0, y1))), y2))), z1))) -> c9(MARK(and(length(s(cons(length(length(cons(y0, y1))), y2))), z1))) MARK(length(and(length(s(cons(length(length(s(y0))), y1))), z1))) -> c9(MARK(and(length(s(cons(length(length(s(y0))), y1))), z1))) MARK(length(and(length(s(cons(length(length(y0)), y1))), z1))) -> c9(MARK(and(length(s(cons(length(length(y0)), y1))), z1))) MARK(length(and(length(s(cons(length(zeros), y0))), z1))) -> c9(MARK(and(length(s(cons(length(zeros), y0))), z1))) S tuples: A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, 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A__LENGTH(cons(z0, and(tt, length(and(zeros, y0))))) -> c5(MARK(and(tt, length(and(zeros, y0))))) A__LENGTH(cons(z0, and(tt, length(length(zeros))))) -> c5(MARK(and(tt, length(length(zeros))))) A__LENGTH(cons(z0, and(tt, length(length(and(y0, y1)))))) -> c5(MARK(and(tt, length(length(and(y0, y1)))))) A__LENGTH(cons(z0, and(tt, length(length(length(y0)))))) -> c5(MARK(and(tt, length(length(length(y0)))))) A__LENGTH(cons(z0, and(tt, length(length(cons(y0, y1)))))) -> c5(MARK(and(tt, length(length(cons(y0, y1)))))) A__LENGTH(cons(z0, and(tt, length(length(s(y0)))))) -> c5(MARK(and(tt, length(length(s(y0)))))) A__LENGTH(cons(z0, and(tt, length(length(y0))))) -> c5(MARK(and(tt, length(length(y0))))) A__LENGTH(cons(z0, and(tt, length(zeros)))) -> c5(MARK(and(tt, length(zeros)))) A__LENGTH(cons(z0, and(s(s(y0)), z2))) -> c5(MARK(and(s(s(y0)), z2))) A__LENGTH(cons(z0, and(s(and(cons(y0, y1), y2)), z2))) -> c5(MARK(and(s(and(cons(y0, y1), y2)), z2))) A__LENGTH(cons(z0, and(s(and(tt, y0)), z2))) -> c5(MARK(and(s(and(tt, y0)), z2))) A__LENGTH(cons(z0, and(s(and(s(y0), y1)), z2))) -> c5(MARK(and(s(and(s(y0), y1)), z2))) A__LENGTH(cons(z0, and(s(length(cons(y0, y1))), z2))) -> c5(MARK(and(s(length(cons(y0, y1))), z2))) A__LENGTH(cons(z0, and(s(length(s(y0))), z2))) -> c5(MARK(and(s(length(s(y0))), z2))) A__LENGTH(cons(z0, and(s(and(and(and(y0, y1), y2), y3)), z2))) -> c5(MARK(and(s(and(and(and(y0, y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(and(and(length(y0), y1), y2)), z2))) -> c5(MARK(and(s(and(and(length(y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(and(and(cons(y0, y1), y2), y3)), z2))) -> c5(MARK(and(s(and(and(cons(y0, y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(and(and(tt, y0), y1)), z2))) -> c5(MARK(and(s(and(and(tt, y0), y1)), z2))) A__LENGTH(cons(z0, and(s(and(and(s(y0), y1), y2)), z2))) -> c5(MARK(and(s(and(and(s(y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(and(and(y0, y1), y2)), z2))) -> c5(MARK(and(s(and(and(y0, y1), y2)), z2))) A__LENGTH(cons(z0, and(s(and(length(zeros), y0)), z2))) -> c5(MARK(and(s(and(length(zeros), y0)), z2))) A__LENGTH(cons(z0, and(s(and(length(and(y0, y1)), y2)), z2))) -> c5(MARK(and(s(and(length(and(y0, y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(and(length(length(y0)), y1)), z2))) -> c5(MARK(and(s(and(length(length(y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(and(length(cons(y0, y1)), y2)), z2))) -> c5(MARK(and(s(and(length(cons(y0, y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(and(length(s(y0)), y1)), z2))) -> c5(MARK(and(s(and(length(s(y0)), y1)), z2))) A__LENGTH(cons(z0, and(s(and(length(y0), y1)), z2))) -> c5(MARK(and(s(and(length(y0), y1)), z2))) A__LENGTH(cons(z0, and(s(and(and(zeros, y0), y1)), z2))) -> c5(MARK(and(s(and(and(zeros, y0), y1)), z2))) A__LENGTH(cons(z0, and(s(length(and(and(y0, y1), y2))), z2))) -> c5(MARK(and(s(length(and(and(y0, y1), y2))), z2))) A__LENGTH(cons(z0, and(s(length(and(length(y0), y1))), z2))) -> c5(MARK(and(s(length(and(length(y0), y1))), z2))) A__LENGTH(cons(z0, 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z2))) -> c5(MARK(and(s(length(length(s(y0)))), z2))) A__LENGTH(cons(z0, and(s(length(length(y0))), z2))) -> c5(MARK(and(s(length(length(y0))), z2))) A__LENGTH(cons(z0, and(s(length(zeros)), z2))) -> c5(MARK(and(s(length(zeros)), z2))) A__LENGTH(cons(z0, and(s(cons(cons(y0, y1), y2)), z2))) -> c5(MARK(and(s(cons(cons(y0, y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(s(y0), y1)), z2))) -> c5(MARK(and(s(cons(s(y0), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(and(cons(y0, y1), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(cons(y0, y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(tt, y0), y1)), z2))) -> c5(MARK(and(s(cons(and(tt, y0), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(and(s(y0), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(s(y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(cons(y0, y1)), y2)), z2))) -> c5(MARK(and(s(cons(length(cons(y0, y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(s(y0)), y1)), z2))) -> c5(MARK(and(s(cons(length(s(y0)), y1)), z2))) 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c5(MARK(and(s(cons(and(length(and(y0, y1)), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(length(y0)), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(length(length(y0)), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(cons(y0, y1)), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(length(cons(y0, y1)), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(s(y0)), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(length(s(y0)), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(and(length(y0), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(length(y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(and(and(zeros, y0), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(and(zeros, y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(and(y0, y1), y2)), y3)), z2))) -> c5(MARK(and(s(cons(length(and(and(y0, y1), y2)), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(length(and(length(y0), y1)), y2)), z2))) -> c5(MARK(and(s(cons(length(and(length(y0), y1)), y2)), z2))) A__LENGTH(cons(z0, 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A__LENGTH(cons(z0, length(and(y0, y1)))) -> c5(MARK(length(and(y0, y1)))) A__LENGTH(cons(z0, length(and(zeros, y0)))) -> c5(MARK(length(and(zeros, y0)))) A__LENGTH(cons(z0, length(length(zeros)))) -> c5(MARK(length(length(zeros)))) A__LENGTH(cons(z0, length(length(and(y0, y1))))) -> c5(MARK(length(length(and(y0, y1))))) A__LENGTH(cons(z0, length(length(length(y0))))) -> c5(MARK(length(length(length(y0))))) A__LENGTH(cons(z0, length(length(cons(y0, y1))))) -> c5(MARK(length(length(cons(y0, y1))))) A__LENGTH(cons(z0, length(length(s(y0))))) -> c5(MARK(length(length(s(y0))))) A__LENGTH(cons(z0, length(length(y0)))) -> c5(MARK(length(length(y0)))) A__LENGTH(cons(z0, length(zeros))) -> c5(MARK(length(zeros))) A__LENGTH(cons(z0, length(s(s(y0))))) -> c5(MARK(length(s(s(y0))))) A__LENGTH(cons(z0, length(s(and(cons(y0, y1), y2))))) -> c5(MARK(length(s(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, length(s(and(tt, y0))))) -> c5(MARK(length(s(and(tt, y0))))) A__LENGTH(cons(z0, length(s(and(s(y0), 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c5(MARK(length(s(cons(and(length(length(y0)), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(and(length(cons(y0, y1)), y2), y3))))) -> c5(MARK(length(s(cons(and(length(cons(y0, y1)), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(length(s(y0)), y1), y2))))) -> c5(MARK(length(s(cons(and(length(s(y0)), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(and(length(y0), y1), y2))))) -> c5(MARK(length(s(cons(and(length(y0), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(and(and(zeros, y0), y1), y2))))) -> c5(MARK(length(s(cons(and(and(zeros, y0), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(length(and(and(y0, y1), y2)), y3))))) -> c5(MARK(length(s(cons(length(and(and(y0, y1), y2)), y3))))) A__LENGTH(cons(z0, length(s(cons(length(and(length(y0), y1)), y2))))) -> c5(MARK(length(s(cons(length(and(length(y0), y1)), y2))))) A__LENGTH(cons(z0, length(s(cons(length(and(cons(y0, y1), y2)), y3))))) -> c5(MARK(length(s(cons(length(and(cons(y0, y1), y2)), y3))))) A__LENGTH(cons(z0, 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MARK(and(and(cons(and(length(length(y0)), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(length(length(y0)), y1), y2), z1))) MARK(and(and(cons(and(length(cons(y0, y1)), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(length(cons(y0, y1)), y2), y3), z1))) MARK(and(and(cons(and(length(s(y0)), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(length(s(y0)), y1), y2), z1))) MARK(and(and(cons(and(length(y0), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(length(y0), y1), y2), z1))) MARK(and(and(cons(and(and(zeros, y0), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(and(zeros, y0), y1), y2), z1))) MARK(and(and(cons(length(and(and(y0, y1), y2)), y3), z1), z2)) -> c8(MARK(and(cons(length(and(and(y0, y1), y2)), y3), z1))) MARK(and(and(cons(length(and(length(y0), y1)), y2), z1), z2)) -> c8(MARK(and(cons(length(and(length(y0), y1)), y2), z1))) MARK(and(and(cons(length(and(cons(y0, y1), y2)), y3), z1), z2)) -> c8(MARK(and(cons(length(and(cons(y0, y1), y2)), y3), z1))) MARK(and(and(cons(length(and(tt, y0)), y1), z1), z2)) -> c8(MARK(and(cons(length(and(tt, y0)), y1), z1))) MARK(and(and(cons(length(and(s(y0), y1)), y2), z1), z2)) -> c8(MARK(and(cons(length(and(s(y0), y1)), y2), z1))) MARK(and(and(cons(length(and(y0, y1)), y2), z1), z2)) -> c8(MARK(and(cons(length(and(y0, y1)), y2), z1))) MARK(and(and(cons(length(and(zeros, y0)), y1), z1), z2)) -> c8(MARK(and(cons(length(and(zeros, y0)), y1), z1))) MARK(and(and(cons(length(length(zeros)), y0), z1), z2)) -> c8(MARK(and(cons(length(length(zeros)), y0), z1))) MARK(and(and(cons(length(length(and(y0, y1))), y2), z1), z2)) -> c8(MARK(and(cons(length(length(and(y0, y1))), y2), z1))) MARK(and(and(cons(length(length(length(y0))), y1), z1), z2)) -> c8(MARK(and(cons(length(length(length(y0))), y1), z1))) MARK(and(and(cons(length(length(cons(y0, y1))), y2), z1), z2)) -> c8(MARK(and(cons(length(length(cons(y0, y1))), y2), z1))) MARK(and(and(cons(length(length(s(y0))), y1), z1), z2)) -> c8(MARK(and(cons(length(length(s(y0))), y1), z1))) MARK(and(and(cons(length(length(y0)), y1), z1), z2)) -> c8(MARK(and(cons(length(length(y0)), y1), z1))) MARK(and(and(cons(length(zeros), y0), z1), z2)) -> c8(MARK(and(cons(length(zeros), y0), z1))) MARK(and(and(tt, cons(y0, y1)), z2)) -> c8(MARK(and(tt, cons(y0, y1)))) MARK(and(and(tt, s(y0)), z2)) -> c8(MARK(and(tt, s(y0)))) MARK(and(and(tt, and(cons(y0, y1), y2)), z2)) -> c8(MARK(and(tt, and(cons(y0, y1), y2)))) MARK(and(and(tt, and(tt, y0)), z2)) -> c8(MARK(and(tt, and(tt, y0)))) MARK(and(and(tt, and(s(y0), y1)), z2)) -> c8(MARK(and(tt, and(s(y0), y1)))) MARK(and(and(tt, length(cons(y0, y1))), z2)) -> c8(MARK(and(tt, length(cons(y0, y1))))) MARK(and(and(tt, length(s(y0))), z2)) -> c8(MARK(and(tt, length(s(y0))))) MARK(and(and(tt, and(and(and(y0, y1), y2), y3)), z2)) -> c8(MARK(and(tt, and(and(and(y0, y1), y2), y3)))) MARK(and(and(tt, and(and(length(y0), y1), y2)), z2)) -> c8(MARK(and(tt, and(and(length(y0), y1), y2)))) MARK(and(and(tt, and(and(cons(y0, y1), y2), y3)), z2)) -> 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MARK(and(and(tt, length(and(and(y0, y1), y2))), z2)) -> c8(MARK(and(tt, length(and(and(y0, y1), y2))))) MARK(and(and(tt, length(and(length(y0), y1))), z2)) -> c8(MARK(and(tt, length(and(length(y0), y1))))) MARK(and(and(tt, length(and(cons(y0, y1), y2))), z2)) -> c8(MARK(and(tt, length(and(cons(y0, y1), y2))))) MARK(and(and(tt, length(and(tt, y0))), z2)) -> c8(MARK(and(tt, length(and(tt, y0))))) MARK(and(and(tt, length(and(s(y0), y1))), z2)) -> c8(MARK(and(tt, length(and(s(y0), y1))))) MARK(and(and(tt, length(and(y0, y1))), z2)) -> c8(MARK(and(tt, length(and(y0, y1))))) MARK(and(and(tt, length(and(zeros, y0))), z2)) -> c8(MARK(and(tt, length(and(zeros, y0))))) MARK(and(and(tt, length(length(zeros))), z2)) -> c8(MARK(and(tt, length(length(zeros))))) MARK(and(and(tt, length(length(and(y0, y1)))), z2)) -> c8(MARK(and(tt, length(length(and(y0, y1)))))) MARK(and(and(tt, length(length(length(y0)))), z2)) -> c8(MARK(and(tt, length(length(length(y0)))))) MARK(and(and(tt, length(length(cons(y0, 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z1))) MARK(length(and(and(s(length(and(y0, y1))), y2), z1))) -> c9(MARK(and(and(s(length(and(y0, y1))), y2), z1))) MARK(length(and(and(s(length(and(zeros, y0))), y1), z1))) -> c9(MARK(and(and(s(length(and(zeros, y0))), y1), z1))) MARK(length(and(and(s(length(length(zeros))), y0), z1))) -> c9(MARK(and(and(s(length(length(zeros))), y0), z1))) MARK(length(and(and(s(length(length(and(y0, y1)))), y2), z1))) -> c9(MARK(and(and(s(length(length(and(y0, y1)))), y2), z1))) MARK(length(and(and(s(length(length(length(y0)))), y1), z1))) -> c9(MARK(and(and(s(length(length(length(y0)))), y1), z1))) MARK(length(and(and(s(length(length(cons(y0, y1)))), y2), z1))) -> c9(MARK(and(and(s(length(length(cons(y0, y1)))), y2), z1))) MARK(length(and(and(s(length(length(s(y0)))), y1), z1))) -> c9(MARK(and(and(s(length(length(s(y0)))), y1), z1))) MARK(length(and(and(s(length(length(y0))), y1), z1))) -> c9(MARK(and(and(s(length(length(y0))), y1), z1))) MARK(length(and(and(s(length(zeros)), y0), z1))) -> c9(MARK(and(and(s(length(zeros)), y0), z1))) MARK(length(and(and(s(cons(cons(y0, y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(cons(y0, y1), y2)), y3), z1))) MARK(length(and(and(s(cons(s(y0), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(s(y0), y1)), y2), z1))) MARK(length(and(and(s(cons(and(cons(y0, y1), y2), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(and(cons(y0, y1), y2), y3)), y4), z1))) MARK(length(and(and(s(cons(and(tt, y0), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(and(tt, y0), y1)), y2), z1))) MARK(length(and(and(s(cons(and(s(y0), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(and(s(y0), y1), y2)), y3), z1))) MARK(length(and(and(s(cons(length(cons(y0, y1)), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(length(cons(y0, y1)), y2)), y3), z1))) MARK(length(and(and(s(cons(length(s(y0)), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(length(s(y0)), y1)), y2), z1))) MARK(length(and(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), y5), z1))) -> c9(MARK(and(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), y5), z1))) MARK(length(and(and(s(cons(and(and(length(y0), y1), y2), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(and(and(length(y0), y1), y2), y3)), y4), z1))) MARK(length(and(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), y5), z1))) -> c9(MARK(and(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), y5), z1))) MARK(length(and(and(s(cons(and(and(tt, y0), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(and(and(tt, y0), y1), y2)), y3), z1))) MARK(length(and(and(s(cons(and(and(s(y0), y1), y2), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(and(and(s(y0), y1), y2), y3)), y4), z1))) MARK(length(and(and(s(cons(and(and(y0, y1), y2), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(and(and(y0, y1), y2), y3)), y4), z1))) MARK(length(and(and(s(cons(and(length(zeros), y0), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(and(length(zeros), y0), y1)), y2), z1))) MARK(length(and(and(s(cons(and(length(and(y0, y1)), y2), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(and(length(and(y0, y1)), y2), y3)), y4), z1))) MARK(length(and(and(s(cons(and(length(length(y0)), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(and(length(length(y0)), y1), y2)), y3), z1))) MARK(length(and(and(s(cons(and(length(cons(y0, y1)), y2), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(and(length(cons(y0, y1)), y2), y3)), y4), z1))) MARK(length(and(and(s(cons(and(length(s(y0)), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(and(length(s(y0)), y1), y2)), y3), z1))) MARK(length(and(and(s(cons(and(length(y0), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(and(length(y0), y1), y2)), y3), z1))) MARK(length(and(and(s(cons(and(and(zeros, y0), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(and(and(zeros, y0), y1), y2)), y3), z1))) MARK(length(and(and(s(cons(length(and(and(y0, y1), y2)), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(length(and(and(y0, y1), y2)), y3)), y4), z1))) MARK(length(and(and(s(cons(length(and(length(y0), y1)), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(length(and(length(y0), y1)), y2)), y3), z1))) MARK(length(and(and(s(cons(length(and(cons(y0, y1), y2)), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(length(and(cons(y0, y1), y2)), y3)), y4), z1))) MARK(length(and(and(s(cons(length(and(tt, y0)), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(length(and(tt, y0)), y1)), y2), z1))) MARK(length(and(and(s(cons(length(and(s(y0), y1)), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(length(and(s(y0), y1)), y2)), y3), z1))) MARK(length(and(and(s(cons(length(and(y0, y1)), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(length(and(y0, y1)), y2)), y3), z1))) MARK(length(and(and(s(cons(length(and(zeros, y0)), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(length(and(zeros, y0)), y1)), y2), z1))) MARK(length(and(and(s(cons(length(length(zeros)), y0)), y1), z1))) -> c9(MARK(and(and(s(cons(length(length(zeros)), y0)), y1), z1))) MARK(length(and(and(s(cons(length(length(and(y0, y1))), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(length(length(and(y0, y1))), y2)), y3), z1))) MARK(length(and(and(s(cons(length(length(length(y0))), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(length(length(length(y0))), y1)), y2), z1))) MARK(length(and(and(s(cons(length(length(cons(y0, y1))), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(length(length(cons(y0, y1))), y2)), y3), z1))) MARK(length(and(and(s(cons(length(length(s(y0))), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(length(length(s(y0))), y1)), y2), z1))) MARK(length(and(and(s(cons(length(length(y0)), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(length(length(y0)), y1)), y2), z1))) MARK(length(and(and(s(cons(length(zeros), y0)), y1), z1))) -> c9(MARK(and(and(s(cons(length(zeros), y0)), y1), z1))) MARK(length(and(length(and(and(y0, y1), y2)), z1))) -> c9(MARK(and(length(and(and(y0, y1), y2)), z1))) MARK(length(and(length(and(length(y0), y1)), z1))) -> c9(MARK(and(length(and(length(y0), y1)), z1))) MARK(length(and(length(and(cons(y0, y1), y2)), z1))) -> c9(MARK(and(length(and(cons(y0, y1), y2)), z1))) MARK(length(and(length(and(tt, y0)), z1))) -> c9(MARK(and(length(and(tt, y0)), z1))) MARK(length(and(length(and(s(y0), y1)), z1))) -> c9(MARK(and(length(and(s(y0), y1)), z1))) MARK(length(and(length(and(zeros, y0)), z1))) -> c9(MARK(and(length(and(zeros, y0)), z1))) MARK(length(and(length(length(zeros)), z1))) -> c9(MARK(and(length(length(zeros)), z1))) MARK(length(and(length(length(and(y0, y1))), z1))) -> c9(MARK(and(length(length(and(y0, y1))), z1))) MARK(length(and(length(length(length(y0))), z1))) -> c9(MARK(and(length(length(length(y0))), z1))) MARK(length(and(length(length(cons(y0, y1))), z1))) -> c9(MARK(and(length(length(cons(y0, y1))), z1))) MARK(length(and(length(length(s(y0))), z1))) -> c9(MARK(and(length(length(s(y0))), z1))) MARK(length(and(length(s(s(y0))), z1))) -> c9(MARK(and(length(s(s(y0))), z1))) MARK(length(and(length(s(and(cons(y0, y1), y2))), z1))) -> c9(MARK(and(length(s(and(cons(y0, y1), y2))), z1))) MARK(length(and(length(s(and(tt, y0))), z1))) -> c9(MARK(and(length(s(and(tt, y0))), z1))) MARK(length(and(length(s(and(s(y0), y1))), z1))) -> c9(MARK(and(length(s(and(s(y0), y1))), z1))) MARK(length(and(length(s(length(cons(y0, y1)))), z1))) -> c9(MARK(and(length(s(length(cons(y0, y1)))), z1))) MARK(length(and(length(s(length(s(y0)))), z1))) -> c9(MARK(and(length(s(length(s(y0)))), z1))) MARK(length(and(length(s(and(and(and(y0, y1), y2), y3))), z1))) -> c9(MARK(and(length(s(and(and(and(y0, y1), y2), y3))), z1))) MARK(length(and(length(s(and(and(length(y0), y1), y2))), z1))) -> c9(MARK(and(length(s(and(and(length(y0), y1), y2))), z1))) MARK(length(and(length(s(and(and(cons(y0, y1), y2), y3))), z1))) -> c9(MARK(and(length(s(and(and(cons(y0, y1), y2), y3))), z1))) MARK(length(and(length(s(and(and(tt, y0), y1))), z1))) -> c9(MARK(and(length(s(and(and(tt, y0), y1))), z1))) MARK(length(and(length(s(and(and(s(y0), y1), y2))), z1))) -> c9(MARK(and(length(s(and(and(s(y0), y1), y2))), z1))) MARK(length(and(length(s(and(and(y0, y1), y2))), z1))) -> c9(MARK(and(length(s(and(and(y0, y1), y2))), z1))) MARK(length(and(length(s(and(length(zeros), y0))), z1))) -> c9(MARK(and(length(s(and(length(zeros), y0))), z1))) MARK(length(and(length(s(and(length(and(y0, y1)), y2))), z1))) -> c9(MARK(and(length(s(and(length(and(y0, y1)), y2))), z1))) MARK(length(and(length(s(and(length(length(y0)), y1))), z1))) -> c9(MARK(and(length(s(and(length(length(y0)), y1))), z1))) MARK(length(and(length(s(and(length(cons(y0, y1)), y2))), z1))) -> c9(MARK(and(length(s(and(length(cons(y0, y1)), y2))), z1))) MARK(length(and(length(s(and(length(s(y0)), y1))), z1))) -> c9(MARK(and(length(s(and(length(s(y0)), y1))), z1))) MARK(length(and(length(s(and(length(y0), y1))), z1))) -> c9(MARK(and(length(s(and(length(y0), y1))), z1))) MARK(length(and(length(s(and(and(zeros, y0), y1))), z1))) -> c9(MARK(and(length(s(and(and(zeros, y0), y1))), z1))) MARK(length(and(length(s(length(and(and(y0, y1), y2)))), z1))) -> c9(MARK(and(length(s(length(and(and(y0, y1), y2)))), z1))) MARK(length(and(length(s(length(and(length(y0), y1)))), z1))) -> c9(MARK(and(length(s(length(and(length(y0), y1)))), z1))) MARK(length(and(length(s(length(and(cons(y0, y1), y2)))), z1))) -> c9(MARK(and(length(s(length(and(cons(y0, y1), y2)))), z1))) MARK(length(and(length(s(length(and(tt, y0)))), z1))) -> c9(MARK(and(length(s(length(and(tt, y0)))), z1))) MARK(length(and(length(s(length(and(s(y0), y1)))), z1))) -> c9(MARK(and(length(s(length(and(s(y0), y1)))), z1))) MARK(length(and(length(s(length(and(y0, y1)))), z1))) -> c9(MARK(and(length(s(length(and(y0, y1)))), z1))) MARK(length(and(length(s(length(and(zeros, y0)))), z1))) -> c9(MARK(and(length(s(length(and(zeros, y0)))), z1))) MARK(length(and(length(s(length(length(zeros)))), z1))) -> c9(MARK(and(length(s(length(length(zeros)))), z1))) MARK(length(and(length(s(length(length(and(y0, y1))))), z1))) -> c9(MARK(and(length(s(length(length(and(y0, y1))))), z1))) MARK(length(and(length(s(length(length(length(y0))))), z1))) -> c9(MARK(and(length(s(length(length(length(y0))))), z1))) MARK(length(and(length(s(length(length(cons(y0, y1))))), z1))) -> c9(MARK(and(length(s(length(length(cons(y0, y1))))), z1))) MARK(length(and(length(s(length(length(s(y0))))), z1))) -> c9(MARK(and(length(s(length(length(s(y0))))), z1))) MARK(length(and(length(s(length(length(y0)))), z1))) -> c9(MARK(and(length(s(length(length(y0)))), z1))) MARK(length(and(length(s(length(zeros))), z1))) -> c9(MARK(and(length(s(length(zeros))), z1))) MARK(length(and(length(s(cons(cons(y0, y1), y2))), z1))) -> c9(MARK(and(length(s(cons(cons(y0, y1), y2))), z1))) MARK(length(and(length(s(cons(s(y0), y1))), z1))) -> c9(MARK(and(length(s(cons(s(y0), y1))), z1))) MARK(length(and(length(s(cons(and(cons(y0, y1), y2), y3))), z1))) -> c9(MARK(and(length(s(cons(and(cons(y0, y1), y2), y3))), z1))) MARK(length(and(length(s(cons(and(tt, y0), y1))), z1))) -> c9(MARK(and(length(s(cons(and(tt, y0), y1))), z1))) MARK(length(and(length(s(cons(and(s(y0), y1), y2))), z1))) -> c9(MARK(and(length(s(cons(and(s(y0), y1), y2))), z1))) MARK(length(and(length(s(cons(length(cons(y0, y1)), y2))), z1))) -> c9(MARK(and(length(s(cons(length(cons(y0, y1)), y2))), z1))) MARK(length(and(length(s(cons(length(s(y0)), y1))), z1))) -> c9(MARK(and(length(s(cons(length(s(y0)), y1))), z1))) MARK(length(and(length(s(cons(and(and(and(y0, y1), y2), y3), y4))), z1))) -> c9(MARK(and(length(s(cons(and(and(and(y0, y1), y2), y3), y4))), z1))) MARK(length(and(length(s(cons(and(and(length(y0), y1), y2), y3))), z1))) -> c9(MARK(and(length(s(cons(and(and(length(y0), y1), y2), y3))), z1))) MARK(length(and(length(s(cons(and(and(cons(y0, y1), y2), y3), y4))), z1))) -> c9(MARK(and(length(s(cons(and(and(cons(y0, y1), y2), y3), y4))), z1))) MARK(length(and(length(s(cons(and(and(tt, y0), y1), y2))), z1))) -> c9(MARK(and(length(s(cons(and(and(tt, y0), y1), y2))), z1))) MARK(length(and(length(s(cons(and(and(s(y0), y1), y2), y3))), z1))) -> c9(MARK(and(length(s(cons(and(and(s(y0), y1), y2), y3))), z1))) MARK(length(and(length(s(cons(and(and(y0, y1), y2), y3))), z1))) -> c9(MARK(and(length(s(cons(and(and(y0, y1), y2), y3))), z1))) MARK(length(and(length(s(cons(and(length(zeros), y0), y1))), z1))) -> c9(MARK(and(length(s(cons(and(length(zeros), y0), y1))), z1))) MARK(length(and(length(s(cons(and(length(and(y0, y1)), y2), y3))), z1))) -> c9(MARK(and(length(s(cons(and(length(and(y0, y1)), y2), y3))), z1))) MARK(length(and(length(s(cons(and(length(length(y0)), y1), y2))), z1))) -> c9(MARK(and(length(s(cons(and(length(length(y0)), y1), y2))), z1))) MARK(length(and(length(s(cons(and(length(cons(y0, y1)), y2), y3))), z1))) -> c9(MARK(and(length(s(cons(and(length(cons(y0, y1)), y2), y3))), z1))) MARK(length(and(length(s(cons(and(length(s(y0)), y1), y2))), z1))) -> c9(MARK(and(length(s(cons(and(length(s(y0)), y1), y2))), z1))) MARK(length(and(length(s(cons(and(length(y0), y1), y2))), z1))) -> c9(MARK(and(length(s(cons(and(length(y0), y1), y2))), z1))) MARK(length(and(length(s(cons(and(and(zeros, y0), y1), y2))), z1))) -> c9(MARK(and(length(s(cons(and(and(zeros, y0), y1), y2))), z1))) MARK(length(and(length(s(cons(length(and(and(y0, y1), y2)), y3))), z1))) -> c9(MARK(and(length(s(cons(length(and(and(y0, y1), y2)), y3))), z1))) MARK(length(and(length(s(cons(length(and(length(y0), y1)), y2))), z1))) -> c9(MARK(and(length(s(cons(length(and(length(y0), y1)), y2))), z1))) MARK(length(and(length(s(cons(length(and(cons(y0, y1), y2)), y3))), z1))) -> c9(MARK(and(length(s(cons(length(and(cons(y0, y1), y2)), y3))), z1))) MARK(length(and(length(s(cons(length(and(tt, y0)), y1))), z1))) -> c9(MARK(and(length(s(cons(length(and(tt, y0)), y1))), z1))) MARK(length(and(length(s(cons(length(and(s(y0), y1)), y2))), z1))) -> c9(MARK(and(length(s(cons(length(and(s(y0), y1)), y2))), z1))) MARK(length(and(length(s(cons(length(and(y0, y1)), y2))), z1))) -> c9(MARK(and(length(s(cons(length(and(y0, y1)), y2))), z1))) MARK(length(and(length(s(cons(length(and(zeros, y0)), y1))), z1))) -> c9(MARK(and(length(s(cons(length(and(zeros, y0)), y1))), z1))) MARK(length(and(length(s(cons(length(length(zeros)), y0))), z1))) -> c9(MARK(and(length(s(cons(length(length(zeros)), y0))), z1))) MARK(length(and(length(s(cons(length(length(and(y0, y1))), y2))), z1))) -> c9(MARK(and(length(s(cons(length(length(and(y0, y1))), y2))), z1))) MARK(length(and(length(s(cons(length(length(length(y0))), y1))), z1))) -> c9(MARK(and(length(s(cons(length(length(length(y0))), y1))), z1))) MARK(length(and(length(s(cons(length(length(cons(y0, y1))), y2))), z1))) -> c9(MARK(and(length(s(cons(length(length(cons(y0, y1))), y2))), z1))) MARK(length(and(length(s(cons(length(length(s(y0))), y1))), z1))) -> c9(MARK(and(length(s(cons(length(length(s(y0))), y1))), z1))) MARK(length(and(length(s(cons(length(length(y0)), y1))), z1))) -> c9(MARK(and(length(s(cons(length(length(y0)), y1))), z1))) MARK(length(and(length(s(cons(length(zeros), y0))), z1))) -> c9(MARK(and(length(s(cons(length(zeros), y0))), z1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__LENGTH_1, MARK_1, A__AND_2 Compound Symbols: c5_2, c9_2, c5_1, c8_2, c8_1, c9_1, c2_1, c10_1, c14_1 ---------------------------------------- (191) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(length(length(x0))) -> c9(MARK(length(x0))) by MARK(length(length(cons(y0, y1)))) -> c9(MARK(length(cons(y0, y1)))) MARK(length(length(and(and(y0, y1), y2)))) -> c9(MARK(length(and(and(y0, y1), y2)))) MARK(length(length(and(length(y0), y1)))) -> c9(MARK(length(and(length(y0), y1)))) MARK(length(length(and(cons(y0, y1), y2)))) -> c9(MARK(length(and(cons(y0, y1), y2)))) MARK(length(length(and(tt, y0)))) -> c9(MARK(length(and(tt, y0)))) MARK(length(length(and(s(y0), y1)))) -> c9(MARK(length(and(s(y0), y1)))) MARK(length(length(and(zeros, y0)))) -> c9(MARK(length(and(zeros, y0)))) MARK(length(length(length(zeros)))) -> c9(MARK(length(length(zeros)))) MARK(length(length(length(and(y0, y1))))) -> c9(MARK(length(length(and(y0, y1))))) MARK(length(length(length(length(y0))))) -> c9(MARK(length(length(length(y0))))) MARK(length(length(length(cons(y0, y1))))) -> c9(MARK(length(length(cons(y0, y1))))) MARK(length(length(length(s(y0))))) -> c9(MARK(length(length(s(y0))))) MARK(length(length(length(y0)))) -> c9(MARK(length(length(y0)))) MARK(length(length(zeros))) -> c9(MARK(length(zeros))) MARK(length(length(s(s(y0))))) -> c9(MARK(length(s(s(y0))))) MARK(length(length(s(and(cons(y0, y1), y2))))) -> c9(MARK(length(s(and(cons(y0, y1), y2))))) MARK(length(length(s(and(tt, y0))))) -> c9(MARK(length(s(and(tt, y0))))) MARK(length(length(s(and(s(y0), y1))))) -> c9(MARK(length(s(and(s(y0), y1))))) MARK(length(length(s(length(cons(y0, y1)))))) -> c9(MARK(length(s(length(cons(y0, y1)))))) MARK(length(length(s(length(s(y0)))))) -> c9(MARK(length(s(length(s(y0)))))) MARK(length(length(s(and(and(and(y0, y1), y2), y3))))) -> c9(MARK(length(s(and(and(and(y0, y1), y2), y3))))) MARK(length(length(s(and(and(length(y0), y1), y2))))) -> c9(MARK(length(s(and(and(length(y0), y1), y2))))) MARK(length(length(s(and(and(cons(y0, y1), y2), y3))))) -> c9(MARK(length(s(and(and(cons(y0, y1), y2), y3))))) MARK(length(length(s(and(and(tt, y0), y1))))) -> c9(MARK(length(s(and(and(tt, y0), y1))))) MARK(length(length(s(and(and(s(y0), y1), y2))))) -> c9(MARK(length(s(and(and(s(y0), y1), y2))))) MARK(length(length(s(and(and(y0, y1), y2))))) -> c9(MARK(length(s(and(and(y0, y1), y2))))) MARK(length(length(s(and(length(zeros), y0))))) -> c9(MARK(length(s(and(length(zeros), y0))))) MARK(length(length(s(and(length(and(y0, y1)), y2))))) -> c9(MARK(length(s(and(length(and(y0, y1)), y2))))) MARK(length(length(s(and(length(length(y0)), y1))))) -> c9(MARK(length(s(and(length(length(y0)), y1))))) MARK(length(length(s(and(length(cons(y0, y1)), y2))))) -> c9(MARK(length(s(and(length(cons(y0, y1)), y2))))) MARK(length(length(s(and(length(s(y0)), y1))))) -> c9(MARK(length(s(and(length(s(y0)), y1))))) MARK(length(length(s(and(length(y0), y1))))) -> c9(MARK(length(s(and(length(y0), y1))))) MARK(length(length(s(and(and(zeros, y0), y1))))) -> c9(MARK(length(s(and(and(zeros, y0), y1))))) MARK(length(length(s(length(and(and(y0, y1), y2)))))) -> c9(MARK(length(s(length(and(and(y0, y1), y2)))))) MARK(length(length(s(length(and(length(y0), y1)))))) -> c9(MARK(length(s(length(and(length(y0), y1)))))) MARK(length(length(s(length(and(cons(y0, y1), y2)))))) -> c9(MARK(length(s(length(and(cons(y0, y1), y2)))))) MARK(length(length(s(length(and(tt, y0)))))) -> c9(MARK(length(s(length(and(tt, y0)))))) MARK(length(length(s(length(and(s(y0), y1)))))) -> c9(MARK(length(s(length(and(s(y0), y1)))))) MARK(length(length(s(length(and(y0, y1)))))) -> c9(MARK(length(s(length(and(y0, y1)))))) MARK(length(length(s(length(and(zeros, y0)))))) -> c9(MARK(length(s(length(and(zeros, y0)))))) MARK(length(length(s(length(length(zeros)))))) -> c9(MARK(length(s(length(length(zeros)))))) MARK(length(length(s(length(length(and(y0, y1))))))) -> c9(MARK(length(s(length(length(and(y0, y1))))))) MARK(length(length(s(length(length(length(y0))))))) -> c9(MARK(length(s(length(length(length(y0))))))) MARK(length(length(s(length(length(cons(y0, y1))))))) -> c9(MARK(length(s(length(length(cons(y0, y1))))))) MARK(length(length(s(length(length(s(y0))))))) -> c9(MARK(length(s(length(length(s(y0))))))) MARK(length(length(s(length(length(y0)))))) -> c9(MARK(length(s(length(length(y0)))))) MARK(length(length(s(length(zeros))))) -> c9(MARK(length(s(length(zeros))))) MARK(length(length(s(cons(cons(y0, y1), y2))))) -> c9(MARK(length(s(cons(cons(y0, y1), y2))))) MARK(length(length(s(cons(s(y0), y1))))) -> c9(MARK(length(s(cons(s(y0), y1))))) MARK(length(length(s(cons(and(cons(y0, y1), y2), y3))))) -> c9(MARK(length(s(cons(and(cons(y0, y1), y2), y3))))) MARK(length(length(s(cons(and(tt, y0), y1))))) -> c9(MARK(length(s(cons(and(tt, y0), y1))))) MARK(length(length(s(cons(and(s(y0), y1), y2))))) -> c9(MARK(length(s(cons(and(s(y0), y1), y2))))) MARK(length(length(s(cons(length(cons(y0, y1)), y2))))) -> c9(MARK(length(s(cons(length(cons(y0, y1)), y2))))) MARK(length(length(s(cons(length(s(y0)), y1))))) -> c9(MARK(length(s(cons(length(s(y0)), y1))))) MARK(length(length(s(cons(and(and(and(y0, y1), y2), y3), y4))))) -> c9(MARK(length(s(cons(and(and(and(y0, y1), y2), y3), y4))))) MARK(length(length(s(cons(and(and(length(y0), y1), y2), y3))))) -> c9(MARK(length(s(cons(and(and(length(y0), y1), y2), y3))))) MARK(length(length(s(cons(and(and(cons(y0, y1), y2), y3), y4))))) -> c9(MARK(length(s(cons(and(and(cons(y0, y1), y2), y3), y4))))) MARK(length(length(s(cons(and(and(tt, y0), y1), y2))))) -> c9(MARK(length(s(cons(and(and(tt, y0), y1), y2))))) MARK(length(length(s(cons(and(and(s(y0), y1), y2), y3))))) -> c9(MARK(length(s(cons(and(and(s(y0), y1), y2), y3))))) MARK(length(length(s(cons(and(and(y0, y1), y2), y3))))) -> c9(MARK(length(s(cons(and(and(y0, y1), y2), y3))))) MARK(length(length(s(cons(and(length(zeros), y0), y1))))) -> c9(MARK(length(s(cons(and(length(zeros), y0), y1))))) MARK(length(length(s(cons(and(length(and(y0, y1)), y2), y3))))) -> c9(MARK(length(s(cons(and(length(and(y0, y1)), y2), y3))))) MARK(length(length(s(cons(and(length(length(y0)), y1), y2))))) -> c9(MARK(length(s(cons(and(length(length(y0)), y1), y2))))) MARK(length(length(s(cons(and(length(cons(y0, y1)), y2), y3))))) -> c9(MARK(length(s(cons(and(length(cons(y0, y1)), y2), y3))))) MARK(length(length(s(cons(and(length(s(y0)), y1), y2))))) -> c9(MARK(length(s(cons(and(length(s(y0)), y1), y2))))) MARK(length(length(s(cons(and(length(y0), y1), y2))))) -> c9(MARK(length(s(cons(and(length(y0), y1), y2))))) MARK(length(length(s(cons(and(and(zeros, y0), y1), y2))))) -> c9(MARK(length(s(cons(and(and(zeros, y0), y1), y2))))) MARK(length(length(s(cons(length(and(and(y0, y1), y2)), y3))))) -> c9(MARK(length(s(cons(length(and(and(y0, y1), y2)), y3))))) MARK(length(length(s(cons(length(and(length(y0), y1)), y2))))) -> c9(MARK(length(s(cons(length(and(length(y0), y1)), y2))))) MARK(length(length(s(cons(length(and(cons(y0, y1), y2)), y3))))) -> c9(MARK(length(s(cons(length(and(cons(y0, y1), y2)), y3))))) MARK(length(length(s(cons(length(and(tt, y0)), y1))))) -> c9(MARK(length(s(cons(length(and(tt, y0)), y1))))) MARK(length(length(s(cons(length(and(s(y0), y1)), y2))))) -> c9(MARK(length(s(cons(length(and(s(y0), y1)), y2))))) MARK(length(length(s(cons(length(and(y0, y1)), y2))))) -> c9(MARK(length(s(cons(length(and(y0, y1)), y2))))) MARK(length(length(s(cons(length(and(zeros, y0)), y1))))) -> c9(MARK(length(s(cons(length(and(zeros, y0)), y1))))) MARK(length(length(s(cons(length(length(zeros)), y0))))) -> c9(MARK(length(s(cons(length(length(zeros)), y0))))) MARK(length(length(s(cons(length(length(and(y0, y1))), y2))))) -> c9(MARK(length(s(cons(length(length(and(y0, y1))), y2))))) MARK(length(length(s(cons(length(length(length(y0))), y1))))) -> c9(MARK(length(s(cons(length(length(length(y0))), y1))))) MARK(length(length(s(cons(length(length(cons(y0, y1))), y2))))) -> c9(MARK(length(s(cons(length(length(cons(y0, y1))), y2))))) MARK(length(length(s(cons(length(length(s(y0))), y1))))) -> c9(MARK(length(s(cons(length(length(s(y0))), y1))))) MARK(length(length(s(cons(length(length(y0)), y1))))) -> c9(MARK(length(s(cons(length(length(y0)), y1))))) MARK(length(length(s(cons(length(zeros), y0))))) -> c9(MARK(length(s(cons(length(zeros), y0))))) MARK(length(length(and(and(and(y0, y1), y2), y3)))) -> c9(MARK(length(and(and(and(y0, y1), y2), y3)))) MARK(length(length(and(and(length(y0), y1), y2)))) -> c9(MARK(length(and(and(length(y0), y1), y2)))) MARK(length(length(and(and(cons(y0, y1), y2), y3)))) -> c9(MARK(length(and(and(cons(y0, y1), y2), y3)))) MARK(length(length(and(and(tt, y0), y1)))) -> c9(MARK(length(and(and(tt, y0), y1)))) MARK(length(length(and(and(s(y0), y1), y2)))) -> c9(MARK(length(and(and(s(y0), y1), y2)))) MARK(length(length(and(length(zeros), y0)))) -> c9(MARK(length(and(length(zeros), y0)))) MARK(length(length(and(length(and(y0, y1)), y2)))) -> c9(MARK(length(and(length(and(y0, y1)), y2)))) MARK(length(length(and(length(length(y0)), y1)))) -> c9(MARK(length(and(length(length(y0)), y1)))) MARK(length(length(and(length(cons(y0, y1)), y2)))) -> c9(MARK(length(and(length(cons(y0, y1)), y2)))) MARK(length(length(and(length(s(y0)), y1)))) -> c9(MARK(length(and(length(s(y0)), y1)))) MARK(length(length(and(and(zeros, y0), y1)))) -> c9(MARK(length(and(and(zeros, y0), y1)))) MARK(length(length(and(cons(cons(y0, y1), y2), y3)))) -> c9(MARK(length(and(cons(cons(y0, y1), y2), y3)))) MARK(length(length(and(cons(s(y0), y1), y2)))) -> c9(MARK(length(and(cons(s(y0), y1), y2)))) MARK(length(length(and(cons(and(cons(y0, y1), y2), y3), y4)))) -> c9(MARK(length(and(cons(and(cons(y0, y1), y2), y3), y4)))) MARK(length(length(and(cons(and(tt, y0), y1), y2)))) -> c9(MARK(length(and(cons(and(tt, y0), y1), y2)))) MARK(length(length(and(cons(and(s(y0), y1), y2), y3)))) -> c9(MARK(length(and(cons(and(s(y0), y1), y2), y3)))) MARK(length(length(and(cons(length(cons(y0, y1)), y2), y3)))) -> c9(MARK(length(and(cons(length(cons(y0, y1)), y2), y3)))) MARK(length(length(and(cons(length(s(y0)), y1), y2)))) -> c9(MARK(length(and(cons(length(s(y0)), y1), y2)))) MARK(length(length(and(cons(and(and(and(y0, y1), y2), y3), y4), y5)))) -> c9(MARK(length(and(cons(and(and(and(y0, y1), y2), y3), y4), y5)))) MARK(length(length(and(cons(and(and(length(y0), y1), y2), y3), y4)))) -> c9(MARK(length(and(cons(and(and(length(y0), y1), y2), y3), y4)))) MARK(length(length(and(cons(and(and(cons(y0, y1), y2), y3), y4), y5)))) -> c9(MARK(length(and(cons(and(and(cons(y0, y1), y2), y3), y4), y5)))) MARK(length(length(and(cons(and(and(tt, y0), y1), y2), y3)))) -> c9(MARK(length(and(cons(and(and(tt, y0), y1), y2), y3)))) MARK(length(length(and(cons(and(and(s(y0), y1), y2), y3), y4)))) -> c9(MARK(length(and(cons(and(and(s(y0), y1), y2), y3), y4)))) MARK(length(length(and(cons(and(and(y0, y1), y2), y3), y4)))) -> c9(MARK(length(and(cons(and(and(y0, y1), y2), y3), y4)))) MARK(length(length(and(cons(and(length(zeros), y0), y1), y2)))) -> c9(MARK(length(and(cons(and(length(zeros), y0), y1), y2)))) MARK(length(length(and(cons(and(length(and(y0, y1)), y2), y3), y4)))) -> c9(MARK(length(and(cons(and(length(and(y0, y1)), y2), y3), y4)))) MARK(length(length(and(cons(and(length(length(y0)), y1), y2), y3)))) -> c9(MARK(length(and(cons(and(length(length(y0)), y1), y2), y3)))) MARK(length(length(and(cons(and(length(cons(y0, y1)), y2), y3), y4)))) -> c9(MARK(length(and(cons(and(length(cons(y0, y1)), y2), y3), y4)))) MARK(length(length(and(cons(and(length(s(y0)), y1), y2), y3)))) -> c9(MARK(length(and(cons(and(length(s(y0)), y1), y2), y3)))) MARK(length(length(and(cons(and(length(y0), y1), y2), y3)))) -> c9(MARK(length(and(cons(and(length(y0), y1), y2), y3)))) MARK(length(length(and(cons(and(and(zeros, y0), y1), y2), y3)))) -> c9(MARK(length(and(cons(and(and(zeros, y0), y1), y2), y3)))) MARK(length(length(and(cons(length(and(and(y0, y1), y2)), y3), y4)))) -> c9(MARK(length(and(cons(length(and(and(y0, y1), y2)), y3), y4)))) MARK(length(length(and(cons(length(and(length(y0), y1)), y2), y3)))) -> c9(MARK(length(and(cons(length(and(length(y0), y1)), y2), y3)))) MARK(length(length(and(cons(length(and(cons(y0, y1), y2)), y3), y4)))) -> c9(MARK(length(and(cons(length(and(cons(y0, y1), y2)), y3), y4)))) MARK(length(length(and(cons(length(and(tt, y0)), y1), y2)))) -> c9(MARK(length(and(cons(length(and(tt, y0)), y1), y2)))) MARK(length(length(and(cons(length(and(s(y0), y1)), y2), y3)))) -> c9(MARK(length(and(cons(length(and(s(y0), y1)), y2), y3)))) MARK(length(length(and(cons(length(and(y0, y1)), y2), y3)))) -> c9(MARK(length(and(cons(length(and(y0, y1)), y2), y3)))) MARK(length(length(and(cons(length(and(zeros, y0)), y1), y2)))) -> c9(MARK(length(and(cons(length(and(zeros, y0)), y1), y2)))) MARK(length(length(and(cons(length(length(zeros)), y0), y1)))) -> c9(MARK(length(and(cons(length(length(zeros)), y0), y1)))) MARK(length(length(and(cons(length(length(and(y0, y1))), y2), y3)))) -> c9(MARK(length(and(cons(length(length(and(y0, y1))), y2), y3)))) MARK(length(length(and(cons(length(length(length(y0))), y1), y2)))) -> c9(MARK(length(and(cons(length(length(length(y0))), y1), y2)))) MARK(length(length(and(cons(length(length(cons(y0, y1))), y2), y3)))) -> c9(MARK(length(and(cons(length(length(cons(y0, y1))), y2), y3)))) MARK(length(length(and(cons(length(length(s(y0))), y1), y2)))) -> c9(MARK(length(and(cons(length(length(s(y0))), y1), y2)))) MARK(length(length(and(cons(length(length(y0)), y1), y2)))) -> c9(MARK(length(and(cons(length(length(y0)), y1), y2)))) MARK(length(length(and(cons(length(zeros), y0), y1)))) -> c9(MARK(length(and(cons(length(zeros), y0), y1)))) MARK(length(length(and(tt, cons(y0, y1))))) -> c9(MARK(length(and(tt, cons(y0, y1))))) MARK(length(length(and(tt, s(y0))))) -> c9(MARK(length(and(tt, s(y0))))) MARK(length(length(and(tt, and(cons(y0, y1), y2))))) -> c9(MARK(length(and(tt, and(cons(y0, y1), y2))))) MARK(length(length(and(tt, and(tt, y0))))) -> c9(MARK(length(and(tt, and(tt, y0))))) MARK(length(length(and(tt, and(s(y0), y1))))) -> c9(MARK(length(and(tt, and(s(y0), y1))))) MARK(length(length(and(tt, length(cons(y0, y1)))))) -> c9(MARK(length(and(tt, length(cons(y0, y1)))))) MARK(length(length(and(tt, length(s(y0)))))) -> c9(MARK(length(and(tt, length(s(y0)))))) MARK(length(length(and(tt, and(and(and(y0, y1), y2), y3))))) -> c9(MARK(length(and(tt, and(and(and(y0, y1), y2), y3))))) MARK(length(length(and(tt, and(and(length(y0), y1), y2))))) -> c9(MARK(length(and(tt, and(and(length(y0), y1), y2))))) MARK(length(length(and(tt, and(and(cons(y0, y1), y2), y3))))) -> c9(MARK(length(and(tt, and(and(cons(y0, y1), y2), y3))))) MARK(length(length(and(tt, and(and(tt, y0), y1))))) -> c9(MARK(length(and(tt, and(and(tt, y0), y1))))) MARK(length(length(and(tt, and(and(s(y0), y1), y2))))) -> c9(MARK(length(and(tt, and(and(s(y0), y1), y2))))) MARK(length(length(and(tt, and(and(y0, y1), y2))))) -> c9(MARK(length(and(tt, and(and(y0, y1), y2))))) MARK(length(length(and(tt, and(length(zeros), y0))))) -> c9(MARK(length(and(tt, and(length(zeros), y0))))) MARK(length(length(and(tt, and(length(and(y0, y1)), y2))))) -> c9(MARK(length(and(tt, and(length(and(y0, y1)), y2))))) MARK(length(length(and(tt, and(length(length(y0)), y1))))) -> c9(MARK(length(and(tt, and(length(length(y0)), y1))))) MARK(length(length(and(tt, and(length(cons(y0, y1)), y2))))) -> c9(MARK(length(and(tt, and(length(cons(y0, y1)), y2))))) MARK(length(length(and(tt, and(length(s(y0)), y1))))) -> c9(MARK(length(and(tt, and(length(s(y0)), 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MARK(length(length(and(tt, length(length(zeros)))))) -> c9(MARK(length(and(tt, length(length(zeros)))))) MARK(length(length(and(tt, length(length(and(y0, y1))))))) -> c9(MARK(length(and(tt, length(length(and(y0, y1))))))) MARK(length(length(and(tt, length(length(length(y0))))))) -> c9(MARK(length(and(tt, length(length(length(y0))))))) MARK(length(length(and(tt, length(length(cons(y0, y1))))))) -> c9(MARK(length(and(tt, length(length(cons(y0, y1))))))) MARK(length(length(and(tt, length(length(s(y0))))))) -> c9(MARK(length(and(tt, length(length(s(y0))))))) MARK(length(length(and(tt, length(length(y0)))))) -> c9(MARK(length(and(tt, length(length(y0)))))) MARK(length(length(and(tt, length(zeros))))) -> c9(MARK(length(and(tt, length(zeros))))) MARK(length(length(and(s(s(y0)), y1)))) -> c9(MARK(length(and(s(s(y0)), y1)))) MARK(length(length(and(s(and(cons(y0, y1), y2)), y3)))) -> c9(MARK(length(and(s(and(cons(y0, y1), y2)), y3)))) MARK(length(length(and(s(and(tt, y0)), y1)))) -> 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-> c9(MARK(length(and(s(length(length(length(y0)))), y1)))) MARK(length(length(and(s(length(length(cons(y0, y1)))), y2)))) -> c9(MARK(length(and(s(length(length(cons(y0, y1)))), y2)))) MARK(length(length(and(s(length(length(s(y0)))), y1)))) -> c9(MARK(length(and(s(length(length(s(y0)))), y1)))) MARK(length(length(and(s(length(length(y0))), y1)))) -> c9(MARK(length(and(s(length(length(y0))), y1)))) MARK(length(length(and(s(length(zeros)), y0)))) -> c9(MARK(length(and(s(length(zeros)), y0)))) MARK(length(length(and(s(cons(cons(y0, y1), y2)), y3)))) -> c9(MARK(length(and(s(cons(cons(y0, y1), y2)), y3)))) MARK(length(length(and(s(cons(s(y0), y1)), y2)))) -> c9(MARK(length(and(s(cons(s(y0), y1)), y2)))) MARK(length(length(and(s(cons(and(cons(y0, y1), y2), y3)), y4)))) -> c9(MARK(length(and(s(cons(and(cons(y0, y1), y2), y3)), y4)))) MARK(length(length(and(s(cons(and(tt, y0), y1)), y2)))) -> c9(MARK(length(and(s(cons(and(tt, y0), y1)), y2)))) MARK(length(length(and(s(cons(and(s(y0), y1), 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MARK(length(length(and(s(cons(and(and(zeros, y0), y1), y2)), y3)))) -> c9(MARK(length(and(s(cons(and(and(zeros, y0), y1), y2)), y3)))) MARK(length(length(and(s(cons(length(and(and(y0, y1), y2)), y3)), y4)))) -> c9(MARK(length(and(s(cons(length(and(and(y0, y1), y2)), y3)), y4)))) MARK(length(length(and(s(cons(length(and(length(y0), y1)), y2)), y3)))) -> c9(MARK(length(and(s(cons(length(and(length(y0), y1)), y2)), y3)))) MARK(length(length(and(s(cons(length(and(cons(y0, y1), y2)), y3)), y4)))) -> c9(MARK(length(and(s(cons(length(and(cons(y0, y1), y2)), y3)), y4)))) MARK(length(length(and(s(cons(length(and(tt, y0)), y1)), y2)))) -> c9(MARK(length(and(s(cons(length(and(tt, y0)), y1)), y2)))) MARK(length(length(and(s(cons(length(and(s(y0), y1)), y2)), y3)))) -> c9(MARK(length(and(s(cons(length(and(s(y0), y1)), y2)), y3)))) MARK(length(length(and(s(cons(length(and(y0, y1)), y2)), y3)))) -> c9(MARK(length(and(s(cons(length(and(y0, y1)), y2)), y3)))) MARK(length(length(and(s(cons(length(and(zeros, y0)), y1)), y2)))) -> c9(MARK(length(and(s(cons(length(and(zeros, y0)), y1)), y2)))) MARK(length(length(and(s(cons(length(length(zeros)), y0)), y1)))) -> c9(MARK(length(and(s(cons(length(length(zeros)), y0)), y1)))) MARK(length(length(and(s(cons(length(length(and(y0, y1))), y2)), y3)))) -> c9(MARK(length(and(s(cons(length(length(and(y0, y1))), y2)), y3)))) MARK(length(length(and(s(cons(length(length(length(y0))), y1)), y2)))) -> c9(MARK(length(and(s(cons(length(length(length(y0))), y1)), y2)))) MARK(length(length(and(s(cons(length(length(cons(y0, y1))), y2)), y3)))) -> c9(MARK(length(and(s(cons(length(length(cons(y0, y1))), y2)), y3)))) MARK(length(length(and(s(cons(length(length(s(y0))), y1)), y2)))) -> c9(MARK(length(and(s(cons(length(length(s(y0))), y1)), y2)))) MARK(length(length(and(s(cons(length(length(y0)), y1)), y2)))) -> c9(MARK(length(and(s(cons(length(length(y0)), y1)), y2)))) MARK(length(length(and(s(cons(length(zeros), y0)), 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MARK(length(length(and(and(length(cons(y0, y1)), y2), y3)))) -> c9(MARK(length(and(and(length(cons(y0, y1)), y2), y3)))) MARK(length(length(and(and(length(s(y0)), y1), y2)))) -> c9(MARK(length(and(and(length(s(y0)), y1), y2)))) MARK(length(length(and(and(and(zeros, y0), y1), y2)))) -> c9(MARK(length(and(and(and(zeros, y0), y1), y2)))) MARK(length(length(and(and(cons(cons(y0, y1), y2), y3), y4)))) -> c9(MARK(length(and(and(cons(cons(y0, y1), y2), y3), y4)))) MARK(length(length(and(and(cons(s(y0), y1), y2), y3)))) -> c9(MARK(length(and(and(cons(s(y0), y1), y2), y3)))) MARK(length(length(and(and(cons(and(cons(y0, y1), y2), y3), y4), y5)))) -> c9(MARK(length(and(and(cons(and(cons(y0, y1), y2), y3), y4), y5)))) MARK(length(length(and(and(cons(and(tt, y0), y1), y2), y3)))) -> c9(MARK(length(and(and(cons(and(tt, y0), y1), y2), y3)))) MARK(length(length(and(and(cons(and(s(y0), y1), y2), y3), y4)))) -> c9(MARK(length(and(and(cons(and(s(y0), y1), y2), y3), y4)))) MARK(length(length(and(and(cons(length(cons(y0, y1)), y2), y3), y4)))) -> c9(MARK(length(and(and(cons(length(cons(y0, y1)), y2), y3), y4)))) MARK(length(length(and(and(cons(length(s(y0)), y1), y2), y3)))) -> c9(MARK(length(and(and(cons(length(s(y0)), y1), y2), y3)))) MARK(length(length(and(and(cons(and(and(and(y0, y1), y2), y3), y4), y5), y6)))) -> c9(MARK(length(and(and(cons(and(and(and(y0, y1), y2), y3), y4), y5), y6)))) MARK(length(length(and(and(cons(and(and(length(y0), y1), y2), y3), y4), y5)))) -> c9(MARK(length(and(and(cons(and(and(length(y0), y1), y2), y3), y4), y5)))) MARK(length(length(and(and(cons(and(and(cons(y0, y1), y2), y3), y4), y5), y6)))) -> c9(MARK(length(and(and(cons(and(and(cons(y0, y1), y2), y3), y4), y5), y6)))) MARK(length(length(and(and(cons(and(and(tt, y0), y1), y2), y3), y4)))) -> c9(MARK(length(and(and(cons(and(and(tt, y0), y1), y2), y3), y4)))) MARK(length(length(and(and(cons(and(and(s(y0), y1), y2), y3), y4), y5)))) -> 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MARK(length(length(and(and(cons(and(length(y0), y1), y2), y3), y4)))) -> c9(MARK(length(and(and(cons(and(length(y0), y1), y2), y3), y4)))) MARK(length(length(and(and(cons(and(and(zeros, y0), y1), y2), y3), y4)))) -> c9(MARK(length(and(and(cons(and(and(zeros, y0), y1), y2), y3), y4)))) MARK(length(length(and(and(cons(length(and(and(y0, y1), y2)), y3), y4), y5)))) -> c9(MARK(length(and(and(cons(length(and(and(y0, y1), y2)), y3), y4), y5)))) MARK(length(length(and(and(cons(length(and(length(y0), y1)), y2), y3), y4)))) -> c9(MARK(length(and(and(cons(length(and(length(y0), y1)), y2), y3), y4)))) MARK(length(length(and(and(cons(length(and(cons(y0, y1), y2)), y3), y4), y5)))) -> c9(MARK(length(and(and(cons(length(and(cons(y0, y1), y2)), y3), y4), y5)))) MARK(length(length(and(and(cons(length(and(tt, y0)), y1), y2), y3)))) -> c9(MARK(length(and(and(cons(length(and(tt, y0)), y1), y2), y3)))) MARK(length(length(and(and(cons(length(and(s(y0), y1)), y2), y3), y4)))) -> c9(MARK(length(and(and(cons(length(and(s(y0), y1)), y2), y3), y4)))) MARK(length(length(and(and(cons(length(and(y0, y1)), y2), y3), y4)))) -> c9(MARK(length(and(and(cons(length(and(y0, y1)), y2), y3), y4)))) MARK(length(length(and(and(cons(length(and(zeros, y0)), y1), y2), y3)))) -> c9(MARK(length(and(and(cons(length(and(zeros, y0)), y1), y2), y3)))) MARK(length(length(and(and(cons(length(length(zeros)), y0), y1), y2)))) -> c9(MARK(length(and(and(cons(length(length(zeros)), y0), y1), y2)))) MARK(length(length(and(and(cons(length(length(and(y0, y1))), y2), y3), y4)))) -> c9(MARK(length(and(and(cons(length(length(and(y0, y1))), y2), y3), y4)))) MARK(length(length(and(and(cons(length(length(length(y0))), y1), y2), y3)))) -> c9(MARK(length(and(and(cons(length(length(length(y0))), y1), y2), y3)))) MARK(length(length(and(and(cons(length(length(cons(y0, y1))), y2), y3), y4)))) -> c9(MARK(length(and(and(cons(length(length(cons(y0, y1))), y2), y3), y4)))) 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c9(MARK(length(and(length(s(and(length(zeros), y0))), y1)))) MARK(length(length(and(length(s(and(length(and(y0, y1)), y2))), y3)))) -> c9(MARK(length(and(length(s(and(length(and(y0, y1)), y2))), y3)))) MARK(length(length(and(length(s(and(length(length(y0)), y1))), y2)))) -> c9(MARK(length(and(length(s(and(length(length(y0)), y1))), y2)))) MARK(length(length(and(length(s(and(length(cons(y0, y1)), y2))), y3)))) -> c9(MARK(length(and(length(s(and(length(cons(y0, y1)), y2))), y3)))) MARK(length(length(and(length(s(and(length(s(y0)), y1))), y2)))) -> c9(MARK(length(and(length(s(and(length(s(y0)), y1))), y2)))) MARK(length(length(and(length(s(and(length(y0), y1))), y2)))) -> c9(MARK(length(and(length(s(and(length(y0), y1))), y2)))) MARK(length(length(and(length(s(and(and(zeros, y0), y1))), y2)))) -> c9(MARK(length(and(length(s(and(and(zeros, y0), y1))), y2)))) MARK(length(length(and(length(s(length(and(and(y0, y1), y2)))), y3)))) -> c9(MARK(length(and(length(s(length(and(and(y0, y1), y2)))), y3)))) MARK(length(length(and(length(s(length(and(length(y0), y1)))), y2)))) -> c9(MARK(length(and(length(s(length(and(length(y0), y1)))), y2)))) MARK(length(length(and(length(s(length(and(cons(y0, y1), y2)))), y3)))) -> c9(MARK(length(and(length(s(length(and(cons(y0, y1), y2)))), y3)))) MARK(length(length(and(length(s(length(and(tt, y0)))), y1)))) -> c9(MARK(length(and(length(s(length(and(tt, y0)))), y1)))) MARK(length(length(and(length(s(length(and(s(y0), y1)))), y2)))) -> c9(MARK(length(and(length(s(length(and(s(y0), y1)))), y2)))) MARK(length(length(and(length(s(length(and(y0, y1)))), y2)))) -> c9(MARK(length(and(length(s(length(and(y0, y1)))), y2)))) MARK(length(length(and(length(s(length(and(zeros, y0)))), y1)))) -> c9(MARK(length(and(length(s(length(and(zeros, y0)))), y1)))) MARK(length(length(and(length(s(length(length(zeros)))), y0)))) -> c9(MARK(length(and(length(s(length(length(zeros)))), y0)))) MARK(length(length(and(length(s(length(length(and(y0, y1))))), y2)))) -> c9(MARK(length(and(length(s(length(length(and(y0, y1))))), y2)))) MARK(length(length(and(length(s(length(length(length(y0))))), y1)))) -> c9(MARK(length(and(length(s(length(length(length(y0))))), y1)))) MARK(length(length(and(length(s(length(length(cons(y0, y1))))), y2)))) -> c9(MARK(length(and(length(s(length(length(cons(y0, y1))))), y2)))) MARK(length(length(and(length(s(length(length(s(y0))))), y1)))) -> c9(MARK(length(and(length(s(length(length(s(y0))))), y1)))) MARK(length(length(and(length(s(length(length(y0)))), y1)))) -> c9(MARK(length(and(length(s(length(length(y0)))), y1)))) MARK(length(length(and(length(s(length(zeros))), y0)))) -> c9(MARK(length(and(length(s(length(zeros))), y0)))) MARK(length(length(and(length(s(cons(cons(y0, y1), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(cons(y0, y1), y2))), y3)))) MARK(length(length(and(length(s(cons(s(y0), y1))), y2)))) -> c9(MARK(length(and(length(s(cons(s(y0), y1))), y2)))) MARK(length(length(and(length(s(cons(and(cons(y0, y1), y2), y3))), y4)))) -> c9(MARK(length(and(length(s(cons(and(cons(y0, y1), y2), y3))), y4)))) MARK(length(length(and(length(s(cons(and(tt, y0), y1))), y2)))) -> c9(MARK(length(and(length(s(cons(and(tt, y0), y1))), y2)))) MARK(length(length(and(length(s(cons(and(s(y0), y1), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(and(s(y0), y1), y2))), y3)))) MARK(length(length(and(length(s(cons(length(cons(y0, y1)), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(length(cons(y0, y1)), y2))), y3)))) MARK(length(length(and(length(s(cons(length(s(y0)), y1))), y2)))) -> c9(MARK(length(and(length(s(cons(length(s(y0)), y1))), y2)))) MARK(length(length(and(length(s(cons(and(and(and(y0, y1), y2), y3), y4))), y5)))) -> c9(MARK(length(and(length(s(cons(and(and(and(y0, y1), y2), y3), y4))), y5)))) MARK(length(length(and(length(s(cons(and(and(length(y0), y1), y2), y3))), y4)))) -> c9(MARK(length(and(length(s(cons(and(and(length(y0), y1), y2), y3))), y4)))) MARK(length(length(and(length(s(cons(and(and(cons(y0, y1), y2), y3), y4))), y5)))) -> c9(MARK(length(and(length(s(cons(and(and(cons(y0, y1), y2), y3), y4))), y5)))) MARK(length(length(and(length(s(cons(and(and(tt, y0), y1), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(and(and(tt, y0), y1), y2))), y3)))) MARK(length(length(and(length(s(cons(and(and(s(y0), y1), y2), y3))), y4)))) -> c9(MARK(length(and(length(s(cons(and(and(s(y0), y1), y2), y3))), y4)))) MARK(length(length(and(length(s(cons(and(and(y0, y1), y2), y3))), y4)))) -> c9(MARK(length(and(length(s(cons(and(and(y0, y1), y2), y3))), y4)))) MARK(length(length(and(length(s(cons(and(length(zeros), y0), y1))), y2)))) -> c9(MARK(length(and(length(s(cons(and(length(zeros), y0), y1))), y2)))) MARK(length(length(and(length(s(cons(and(length(and(y0, y1)), y2), y3))), y4)))) -> c9(MARK(length(and(length(s(cons(and(length(and(y0, y1)), y2), y3))), y4)))) MARK(length(length(and(length(s(cons(and(length(length(y0)), y1), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(and(length(length(y0)), y1), y2))), y3)))) MARK(length(length(and(length(s(cons(and(length(cons(y0, y1)), y2), y3))), y4)))) -> c9(MARK(length(and(length(s(cons(and(length(cons(y0, y1)), y2), y3))), y4)))) MARK(length(length(and(length(s(cons(and(length(s(y0)), y1), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(and(length(s(y0)), y1), y2))), y3)))) MARK(length(length(and(length(s(cons(and(length(y0), y1), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(and(length(y0), y1), y2))), y3)))) MARK(length(length(and(length(s(cons(and(and(zeros, y0), y1), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(and(and(zeros, y0), y1), y2))), y3)))) MARK(length(length(and(length(s(cons(length(and(and(y0, y1), y2)), y3))), y4)))) -> c9(MARK(length(and(length(s(cons(length(and(and(y0, y1), y2)), y3))), y4)))) MARK(length(length(and(length(s(cons(length(and(length(y0), y1)), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(length(and(length(y0), y1)), y2))), y3)))) MARK(length(length(and(length(s(cons(length(and(cons(y0, y1), y2)), y3))), y4)))) -> c9(MARK(length(and(length(s(cons(length(and(cons(y0, y1), y2)), y3))), y4)))) MARK(length(length(and(length(s(cons(length(and(tt, y0)), y1))), y2)))) -> c9(MARK(length(and(length(s(cons(length(and(tt, y0)), y1))), y2)))) MARK(length(length(and(length(s(cons(length(and(s(y0), y1)), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(length(and(s(y0), y1)), y2))), y3)))) MARK(length(length(and(length(s(cons(length(and(y0, y1)), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(length(and(y0, y1)), y2))), y3)))) MARK(length(length(and(length(s(cons(length(and(zeros, y0)), y1))), y2)))) -> c9(MARK(length(and(length(s(cons(length(and(zeros, y0)), y1))), y2)))) MARK(length(length(and(length(s(cons(length(length(zeros)), y0))), y1)))) -> c9(MARK(length(and(length(s(cons(length(length(zeros)), y0))), y1)))) MARK(length(length(and(length(s(cons(length(length(and(y0, y1))), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(length(length(and(y0, y1))), y2))), y3)))) MARK(length(length(and(length(s(cons(length(length(length(y0))), y1))), y2)))) -> c9(MARK(length(and(length(s(cons(length(length(length(y0))), y1))), y2)))) MARK(length(length(and(length(s(cons(length(length(cons(y0, y1))), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(length(length(cons(y0, y1))), y2))), y3)))) MARK(length(length(and(length(s(cons(length(length(s(y0))), y1))), y2)))) -> c9(MARK(length(and(length(s(cons(length(length(s(y0))), y1))), y2)))) MARK(length(length(and(length(s(cons(length(length(y0)), y1))), y2)))) -> c9(MARK(length(and(length(s(cons(length(length(y0)), y1))), y2)))) MARK(length(length(and(length(s(cons(length(zeros), y0))), y1)))) -> c9(MARK(length(and(length(s(cons(length(zeros), y0))), y1)))) ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(z0) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) 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c14(MARK(length(length(length(y0))))) MARK(s(length(length(cons(y0, y1))))) -> c14(MARK(length(length(cons(y0, y1))))) MARK(s(length(length(s(y0))))) -> c14(MARK(length(length(s(y0))))) MARK(s(length(length(y0)))) -> c14(MARK(length(length(y0)))) MARK(s(length(zeros))) -> c14(MARK(length(zeros))) MARK(s(cons(cons(y0, y1), y2))) -> c14(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c14(MARK(cons(s(y0), y1))) MARK(s(cons(and(cons(y0, y1), y2), y3))) -> c14(MARK(cons(and(cons(y0, y1), y2), y3))) MARK(s(cons(and(tt, y0), y1))) -> c14(MARK(cons(and(tt, y0), y1))) MARK(s(cons(and(s(y0), y1), y2))) -> c14(MARK(cons(and(s(y0), y1), y2))) MARK(s(cons(length(cons(y0, y1)), y2))) -> c14(MARK(cons(length(cons(y0, y1)), y2))) MARK(s(cons(length(s(y0)), y1))) -> c14(MARK(cons(length(s(y0)), y1))) MARK(s(cons(and(and(and(y0, y1), y2), y3), y4))) -> c14(MARK(cons(and(and(and(y0, y1), y2), y3), y4))) MARK(s(cons(and(and(length(y0), y1), y2), y3))) -> c14(MARK(cons(and(and(length(y0), y1), 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c14(MARK(cons(and(and(zeros, y0), y1), y2))) MARK(s(cons(length(and(and(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(and(y0, y1), y2)), y3))) MARK(s(cons(length(and(length(y0), y1)), y2))) -> c14(MARK(cons(length(and(length(y0), y1)), y2))) MARK(s(cons(length(and(cons(y0, y1), y2)), y3))) -> c14(MARK(cons(length(and(cons(y0, y1), y2)), y3))) MARK(s(cons(length(and(tt, y0)), y1))) -> c14(MARK(cons(length(and(tt, y0)), y1))) MARK(s(cons(length(and(s(y0), y1)), y2))) -> c14(MARK(cons(length(and(s(y0), y1)), y2))) MARK(s(cons(length(and(y0, y1)), y2))) -> c14(MARK(cons(length(and(y0, y1)), y2))) MARK(s(cons(length(and(zeros, y0)), y1))) -> c14(MARK(cons(length(and(zeros, y0)), y1))) MARK(s(cons(length(length(zeros)), y0))) -> c14(MARK(cons(length(length(zeros)), y0))) MARK(s(cons(length(length(and(y0, y1))), y2))) -> c14(MARK(cons(length(length(and(y0, y1))), y2))) MARK(s(cons(length(length(length(y0))), y1))) -> c14(MARK(cons(length(length(length(y0))), y1))) 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c5(MARK(s(length(and(and(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(length(y0), y1))))) -> c5(MARK(s(length(and(length(y0), y1))))) A__LENGTH(cons(z0, s(length(and(cons(y0, y1), y2))))) -> c5(MARK(s(length(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, s(length(and(tt, y0))))) -> c5(MARK(s(length(and(tt, y0))))) A__LENGTH(cons(z0, s(length(and(s(y0), y1))))) -> c5(MARK(s(length(and(s(y0), y1))))) A__LENGTH(cons(z0, s(length(and(y0, y1))))) -> c5(MARK(s(length(and(y0, y1))))) A__LENGTH(cons(z0, s(length(and(zeros, y0))))) -> c5(MARK(s(length(and(zeros, y0))))) A__LENGTH(cons(z0, s(length(length(zeros))))) -> c5(MARK(s(length(length(zeros))))) A__LENGTH(cons(z0, s(length(length(and(y0, y1)))))) -> c5(MARK(s(length(length(and(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(length(y0)))))) -> c5(MARK(s(length(length(length(y0)))))) A__LENGTH(cons(z0, s(length(length(cons(y0, y1)))))) -> c5(MARK(s(length(length(cons(y0, y1)))))) A__LENGTH(cons(z0, s(length(length(s(y0)))))) -> c5(MARK(s(length(length(s(y0)))))) A__LENGTH(cons(z0, s(length(length(y0))))) -> c5(MARK(s(length(length(y0))))) A__LENGTH(cons(z0, s(length(zeros)))) -> c5(MARK(s(length(zeros)))) A__LENGTH(cons(z0, s(cons(cons(y0, y1), y2)))) -> c5(MARK(s(cons(cons(y0, y1), y2)))) A__LENGTH(cons(z0, s(cons(s(y0), y1)))) -> c5(MARK(s(cons(s(y0), y1)))) A__LENGTH(cons(z0, s(cons(and(cons(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(tt, y0), y1)))) -> c5(MARK(s(cons(and(tt, y0), y1)))) A__LENGTH(cons(z0, s(cons(and(s(y0), y1), y2)))) -> c5(MARK(s(cons(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(length(cons(y0, y1)), y2)))) -> c5(MARK(s(cons(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, s(cons(length(s(y0)), y1)))) -> c5(MARK(s(cons(length(s(y0)), y1)))) A__LENGTH(cons(z0, s(cons(and(and(and(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(and(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(length(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(length(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(cons(y0, y1), y2), y3), y4)))) -> c5(MARK(s(cons(and(and(cons(y0, y1), y2), y3), y4)))) A__LENGTH(cons(z0, s(cons(and(and(tt, y0), y1), y2)))) -> c5(MARK(s(cons(and(and(tt, y0), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(and(s(y0), y1), y2), y3)))) -> c5(MARK(s(cons(and(and(s(y0), y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(and(y0, y1), y2), y3)))) -> c5(MARK(s(cons(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(zeros), y0), y1)))) -> c5(MARK(s(cons(and(length(zeros), y0), y1)))) A__LENGTH(cons(z0, s(cons(and(length(and(y0, y1)), y2), y3)))) -> c5(MARK(s(cons(and(length(and(y0, y1)), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(length(y0)), y1), y2)))) -> c5(MARK(s(cons(and(length(length(y0)), y1), y2)))) A__LENGTH(cons(z0, s(cons(and(length(cons(y0, y1)), y2), y3)))) -> c5(MARK(s(cons(and(length(cons(y0, y1)), y2), y3)))) A__LENGTH(cons(z0, s(cons(and(length(s(y0)), y1), 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MARK(length(length(length(and(y0, y1))))) -> c9(MARK(length(length(and(y0, y1))))) MARK(length(length(length(length(y0))))) -> c9(MARK(length(length(length(y0))))) MARK(length(length(length(cons(y0, y1))))) -> c9(MARK(length(length(cons(y0, y1))))) MARK(length(length(length(s(y0))))) -> c9(MARK(length(length(s(y0))))) MARK(length(length(length(y0)))) -> c9(MARK(length(length(y0)))) MARK(length(length(zeros))) -> c9(MARK(length(zeros))) MARK(length(length(s(s(y0))))) -> c9(MARK(length(s(s(y0))))) MARK(length(length(s(and(cons(y0, y1), y2))))) -> c9(MARK(length(s(and(cons(y0, y1), y2))))) MARK(length(length(s(and(tt, y0))))) -> c9(MARK(length(s(and(tt, y0))))) MARK(length(length(s(and(s(y0), y1))))) -> c9(MARK(length(s(and(s(y0), y1))))) MARK(length(length(s(length(cons(y0, y1)))))) -> c9(MARK(length(s(length(cons(y0, y1)))))) MARK(length(length(s(length(s(y0)))))) -> c9(MARK(length(s(length(s(y0)))))) MARK(length(length(s(and(and(and(y0, y1), y2), y3))))) -> 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MARK(length(length(s(and(length(s(y0)), y1))))) -> c9(MARK(length(s(and(length(s(y0)), y1))))) MARK(length(length(s(and(length(y0), y1))))) -> c9(MARK(length(s(and(length(y0), y1))))) MARK(length(length(s(and(and(zeros, y0), y1))))) -> c9(MARK(length(s(and(and(zeros, y0), y1))))) MARK(length(length(s(length(and(and(y0, y1), y2)))))) -> c9(MARK(length(s(length(and(and(y0, y1), y2)))))) MARK(length(length(s(length(and(length(y0), y1)))))) -> c9(MARK(length(s(length(and(length(y0), y1)))))) MARK(length(length(s(length(and(cons(y0, y1), y2)))))) -> c9(MARK(length(s(length(and(cons(y0, y1), y2)))))) MARK(length(length(s(length(and(tt, y0)))))) -> c9(MARK(length(s(length(and(tt, y0)))))) MARK(length(length(s(length(and(s(y0), y1)))))) -> c9(MARK(length(s(length(and(s(y0), y1)))))) MARK(length(length(s(length(and(y0, y1)))))) -> c9(MARK(length(s(length(and(y0, y1)))))) MARK(length(length(s(length(and(zeros, y0)))))) -> c9(MARK(length(s(length(and(zeros, y0)))))) MARK(length(length(s(length(length(zeros)))))) -> c9(MARK(length(s(length(length(zeros)))))) MARK(length(length(s(length(length(and(y0, y1))))))) -> c9(MARK(length(s(length(length(and(y0, y1))))))) MARK(length(length(s(length(length(length(y0))))))) -> c9(MARK(length(s(length(length(length(y0))))))) MARK(length(length(s(length(length(cons(y0, y1))))))) -> c9(MARK(length(s(length(length(cons(y0, y1))))))) MARK(length(length(s(length(length(s(y0))))))) -> c9(MARK(length(s(length(length(s(y0))))))) MARK(length(length(s(length(length(y0)))))) -> c9(MARK(length(s(length(length(y0)))))) MARK(length(length(s(length(zeros))))) -> c9(MARK(length(s(length(zeros))))) MARK(length(length(s(cons(cons(y0, y1), y2))))) -> c9(MARK(length(s(cons(cons(y0, y1), y2))))) MARK(length(length(s(cons(s(y0), y1))))) -> c9(MARK(length(s(cons(s(y0), y1))))) MARK(length(length(s(cons(and(cons(y0, y1), y2), y3))))) -> c9(MARK(length(s(cons(and(cons(y0, y1), y2), y3))))) MARK(length(length(s(cons(and(tt, y0), y1))))) -> c9(MARK(length(s(cons(and(tt, y0), y1))))) MARK(length(length(s(cons(and(s(y0), y1), y2))))) -> c9(MARK(length(s(cons(and(s(y0), y1), y2))))) MARK(length(length(s(cons(length(cons(y0, y1)), y2))))) -> c9(MARK(length(s(cons(length(cons(y0, y1)), y2))))) MARK(length(length(s(cons(length(s(y0)), y1))))) -> c9(MARK(length(s(cons(length(s(y0)), y1))))) MARK(length(length(s(cons(and(and(and(y0, y1), y2), y3), y4))))) -> c9(MARK(length(s(cons(and(and(and(y0, y1), y2), y3), y4))))) MARK(length(length(s(cons(and(and(length(y0), y1), y2), y3))))) -> c9(MARK(length(s(cons(and(and(length(y0), y1), y2), y3))))) MARK(length(length(s(cons(and(and(cons(y0, y1), y2), y3), y4))))) -> c9(MARK(length(s(cons(and(and(cons(y0, y1), y2), y3), y4))))) MARK(length(length(s(cons(and(and(tt, y0), y1), y2))))) -> c9(MARK(length(s(cons(and(and(tt, y0), y1), y2))))) MARK(length(length(s(cons(and(and(s(y0), y1), y2), y3))))) -> c9(MARK(length(s(cons(and(and(s(y0), y1), y2), y3))))) 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c9(MARK(length(s(cons(length(length(and(y0, y1))), y2))))) MARK(length(length(s(cons(length(length(length(y0))), y1))))) -> c9(MARK(length(s(cons(length(length(length(y0))), y1))))) MARK(length(length(s(cons(length(length(cons(y0, y1))), y2))))) -> c9(MARK(length(s(cons(length(length(cons(y0, y1))), y2))))) MARK(length(length(s(cons(length(length(s(y0))), y1))))) -> c9(MARK(length(s(cons(length(length(s(y0))), y1))))) MARK(length(length(s(cons(length(length(y0)), y1))))) -> c9(MARK(length(s(cons(length(length(y0)), y1))))) MARK(length(length(s(cons(length(zeros), y0))))) -> c9(MARK(length(s(cons(length(zeros), y0))))) MARK(length(length(and(and(and(y0, y1), y2), y3)))) -> c9(MARK(length(and(and(and(y0, y1), y2), y3)))) MARK(length(length(and(and(length(y0), y1), y2)))) -> c9(MARK(length(and(and(length(y0), y1), y2)))) MARK(length(length(and(and(cons(y0, y1), y2), y3)))) -> c9(MARK(length(and(and(cons(y0, y1), y2), y3)))) MARK(length(length(and(and(tt, y0), y1)))) -> c9(MARK(length(and(and(tt, y0), y1)))) MARK(length(length(and(and(s(y0), y1), y2)))) -> c9(MARK(length(and(and(s(y0), y1), y2)))) MARK(length(length(and(length(zeros), y0)))) -> c9(MARK(length(and(length(zeros), y0)))) MARK(length(length(and(length(and(y0, y1)), y2)))) -> c9(MARK(length(and(length(and(y0, y1)), y2)))) MARK(length(length(and(length(length(y0)), y1)))) -> c9(MARK(length(and(length(length(y0)), y1)))) MARK(length(length(and(length(cons(y0, y1)), y2)))) -> c9(MARK(length(and(length(cons(y0, y1)), y2)))) MARK(length(length(and(length(s(y0)), y1)))) -> c9(MARK(length(and(length(s(y0)), y1)))) MARK(length(length(and(and(zeros, y0), y1)))) -> c9(MARK(length(and(and(zeros, y0), y1)))) MARK(length(length(and(cons(cons(y0, y1), y2), y3)))) -> c9(MARK(length(and(cons(cons(y0, y1), y2), y3)))) MARK(length(length(and(cons(s(y0), y1), y2)))) -> c9(MARK(length(and(cons(s(y0), y1), y2)))) MARK(length(length(and(cons(and(cons(y0, y1), y2), y3), y4)))) -> c9(MARK(length(and(cons(and(cons(y0, y1), y2), y3), y4)))) MARK(length(length(and(cons(and(tt, y0), y1), y2)))) -> c9(MARK(length(and(cons(and(tt, y0), y1), y2)))) MARK(length(length(and(cons(and(s(y0), y1), y2), y3)))) -> c9(MARK(length(and(cons(and(s(y0), y1), y2), y3)))) MARK(length(length(and(cons(length(cons(y0, y1)), y2), y3)))) -> c9(MARK(length(and(cons(length(cons(y0, y1)), y2), y3)))) MARK(length(length(and(cons(length(s(y0)), y1), y2)))) -> c9(MARK(length(and(cons(length(s(y0)), y1), y2)))) MARK(length(length(and(cons(and(and(and(y0, y1), y2), y3), y4), y5)))) -> c9(MARK(length(and(cons(and(and(and(y0, y1), y2), y3), y4), y5)))) MARK(length(length(and(cons(and(and(length(y0), y1), y2), y3), y4)))) -> c9(MARK(length(and(cons(and(and(length(y0), y1), y2), y3), y4)))) MARK(length(length(and(cons(and(and(cons(y0, y1), y2), y3), y4), y5)))) -> c9(MARK(length(and(cons(and(and(cons(y0, y1), y2), y3), y4), y5)))) MARK(length(length(and(cons(and(and(tt, y0), y1), y2), y3)))) -> 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MARK(length(length(and(cons(and(length(y0), y1), y2), y3)))) -> c9(MARK(length(and(cons(and(length(y0), y1), y2), y3)))) MARK(length(length(and(cons(and(and(zeros, y0), y1), y2), y3)))) -> c9(MARK(length(and(cons(and(and(zeros, y0), y1), y2), y3)))) MARK(length(length(and(cons(length(and(and(y0, y1), y2)), y3), y4)))) -> c9(MARK(length(and(cons(length(and(and(y0, y1), y2)), y3), y4)))) MARK(length(length(and(cons(length(and(length(y0), y1)), y2), y3)))) -> c9(MARK(length(and(cons(length(and(length(y0), y1)), y2), y3)))) MARK(length(length(and(cons(length(and(cons(y0, y1), y2)), y3), y4)))) -> c9(MARK(length(and(cons(length(and(cons(y0, y1), y2)), y3), y4)))) MARK(length(length(and(cons(length(and(tt, y0)), y1), y2)))) -> c9(MARK(length(and(cons(length(and(tt, y0)), y1), y2)))) MARK(length(length(and(cons(length(and(s(y0), y1)), y2), y3)))) -> c9(MARK(length(and(cons(length(and(s(y0), y1)), y2), y3)))) MARK(length(length(and(cons(length(and(y0, y1)), y2), y3)))) -> c9(MARK(length(and(cons(length(and(y0, y1)), y2), y3)))) MARK(length(length(and(cons(length(and(zeros, y0)), y1), y2)))) -> c9(MARK(length(and(cons(length(and(zeros, y0)), y1), y2)))) MARK(length(length(and(cons(length(length(zeros)), y0), y1)))) -> c9(MARK(length(and(cons(length(length(zeros)), y0), y1)))) MARK(length(length(and(cons(length(length(and(y0, y1))), y2), y3)))) -> c9(MARK(length(and(cons(length(length(and(y0, y1))), y2), y3)))) MARK(length(length(and(cons(length(length(length(y0))), y1), y2)))) -> c9(MARK(length(and(cons(length(length(length(y0))), y1), y2)))) MARK(length(length(and(cons(length(length(cons(y0, y1))), y2), y3)))) -> c9(MARK(length(and(cons(length(length(cons(y0, y1))), y2), y3)))) MARK(length(length(and(cons(length(length(s(y0))), y1), y2)))) -> c9(MARK(length(and(cons(length(length(s(y0))), y1), y2)))) MARK(length(length(and(cons(length(length(y0)), y1), y2)))) -> c9(MARK(length(and(cons(length(length(y0)), y1), y2)))) MARK(length(length(and(cons(length(zeros), y0), y1)))) -> c9(MARK(length(and(cons(length(zeros), y0), y1)))) MARK(length(length(and(tt, cons(y0, y1))))) -> c9(MARK(length(and(tt, cons(y0, y1))))) MARK(length(length(and(tt, s(y0))))) -> c9(MARK(length(and(tt, s(y0))))) MARK(length(length(and(tt, and(cons(y0, y1), y2))))) -> c9(MARK(length(and(tt, and(cons(y0, y1), y2))))) MARK(length(length(and(tt, and(tt, y0))))) -> c9(MARK(length(and(tt, and(tt, y0))))) MARK(length(length(and(tt, and(s(y0), y1))))) -> c9(MARK(length(and(tt, and(s(y0), y1))))) MARK(length(length(and(tt, length(cons(y0, y1)))))) -> c9(MARK(length(and(tt, length(cons(y0, y1)))))) MARK(length(length(and(tt, length(s(y0)))))) -> c9(MARK(length(and(tt, length(s(y0)))))) MARK(length(length(and(tt, and(and(and(y0, y1), y2), y3))))) -> c9(MARK(length(and(tt, and(and(and(y0, y1), y2), y3))))) MARK(length(length(and(tt, and(and(length(y0), y1), y2))))) -> c9(MARK(length(and(tt, and(and(length(y0), y1), y2))))) MARK(length(length(and(tt, and(and(cons(y0, y1), y2), y3))))) -> c9(MARK(length(and(tt, and(and(cons(y0, y1), y2), y3))))) MARK(length(length(and(tt, and(and(tt, y0), y1))))) -> c9(MARK(length(and(tt, and(and(tt, y0), y1))))) MARK(length(length(and(tt, and(and(s(y0), y1), y2))))) -> c9(MARK(length(and(tt, and(and(s(y0), y1), y2))))) MARK(length(length(and(tt, and(and(y0, y1), y2))))) -> c9(MARK(length(and(tt, and(and(y0, y1), y2))))) MARK(length(length(and(tt, and(length(zeros), y0))))) -> c9(MARK(length(and(tt, and(length(zeros), y0))))) MARK(length(length(and(tt, and(length(and(y0, y1)), y2))))) -> c9(MARK(length(and(tt, and(length(and(y0, y1)), y2))))) MARK(length(length(and(tt, and(length(length(y0)), y1))))) -> c9(MARK(length(and(tt, and(length(length(y0)), y1))))) MARK(length(length(and(tt, and(length(cons(y0, y1)), y2))))) -> c9(MARK(length(and(tt, and(length(cons(y0, y1)), y2))))) MARK(length(length(and(tt, and(length(s(y0)), y1))))) -> c9(MARK(length(and(tt, and(length(s(y0)), y1))))) MARK(length(length(and(tt, and(length(y0), y1))))) -> c9(MARK(length(and(tt, and(length(y0), y1))))) MARK(length(length(and(tt, and(and(zeros, y0), y1))))) -> c9(MARK(length(and(tt, and(and(zeros, y0), y1))))) MARK(length(length(and(tt, length(and(and(y0, y1), y2)))))) -> c9(MARK(length(and(tt, length(and(and(y0, y1), y2)))))) MARK(length(length(and(tt, length(and(length(y0), y1)))))) -> c9(MARK(length(and(tt, length(and(length(y0), y1)))))) MARK(length(length(and(tt, length(and(cons(y0, y1), y2)))))) -> c9(MARK(length(and(tt, length(and(cons(y0, y1), y2)))))) MARK(length(length(and(tt, length(and(tt, y0)))))) -> c9(MARK(length(and(tt, length(and(tt, y0)))))) MARK(length(length(and(tt, length(and(s(y0), y1)))))) -> c9(MARK(length(and(tt, length(and(s(y0), y1)))))) MARK(length(length(and(tt, length(and(y0, y1)))))) -> c9(MARK(length(and(tt, length(and(y0, y1)))))) MARK(length(length(and(tt, length(and(zeros, y0)))))) -> c9(MARK(length(and(tt, length(and(zeros, y0)))))) MARK(length(length(and(tt, length(length(zeros)))))) -> c9(MARK(length(and(tt, length(length(zeros)))))) MARK(length(length(and(tt, length(length(and(y0, y1))))))) -> c9(MARK(length(and(tt, length(length(and(y0, y1))))))) MARK(length(length(and(tt, length(length(length(y0))))))) -> c9(MARK(length(and(tt, length(length(length(y0))))))) MARK(length(length(and(tt, length(length(cons(y0, y1))))))) -> c9(MARK(length(and(tt, length(length(cons(y0, y1))))))) MARK(length(length(and(tt, length(length(s(y0))))))) -> c9(MARK(length(and(tt, length(length(s(y0))))))) MARK(length(length(and(tt, length(length(y0)))))) -> c9(MARK(length(and(tt, length(length(y0)))))) MARK(length(length(and(tt, length(zeros))))) -> c9(MARK(length(and(tt, length(zeros))))) MARK(length(length(and(s(s(y0)), y1)))) -> c9(MARK(length(and(s(s(y0)), y1)))) MARK(length(length(and(s(and(cons(y0, y1), y2)), y3)))) -> c9(MARK(length(and(s(and(cons(y0, y1), y2)), y3)))) MARK(length(length(and(s(and(tt, y0)), y1)))) -> c9(MARK(length(and(s(and(tt, y0)), y1)))) MARK(length(length(and(s(and(s(y0), y1)), y2)))) -> c9(MARK(length(and(s(and(s(y0), y1)), y2)))) MARK(length(length(and(s(length(cons(y0, y1))), y2)))) -> c9(MARK(length(and(s(length(cons(y0, y1))), y2)))) MARK(length(length(and(s(length(s(y0))), y1)))) -> c9(MARK(length(and(s(length(s(y0))), y1)))) MARK(length(length(and(s(and(and(and(y0, y1), y2), y3)), y4)))) -> c9(MARK(length(and(s(and(and(and(y0, y1), y2), y3)), y4)))) MARK(length(length(and(s(and(and(length(y0), y1), y2)), y3)))) -> c9(MARK(length(and(s(and(and(length(y0), y1), y2)), y3)))) MARK(length(length(and(s(and(and(cons(y0, y1), y2), y3)), y4)))) -> c9(MARK(length(and(s(and(and(cons(y0, y1), y2), y3)), y4)))) MARK(length(length(and(s(and(and(tt, y0), y1)), y2)))) -> c9(MARK(length(and(s(and(and(tt, y0), y1)), y2)))) MARK(length(length(and(s(and(and(s(y0), y1), y2)), y3)))) -> c9(MARK(length(and(s(and(and(s(y0), y1), y2)), y3)))) MARK(length(length(and(s(and(and(y0, y1), y2)), y3)))) -> c9(MARK(length(and(s(and(and(y0, y1), y2)), y3)))) MARK(length(length(and(s(and(length(zeros), y0)), y1)))) -> c9(MARK(length(and(s(and(length(zeros), y0)), y1)))) MARK(length(length(and(s(and(length(and(y0, y1)), y2)), y3)))) -> c9(MARK(length(and(s(and(length(and(y0, y1)), y2)), y3)))) MARK(length(length(and(s(and(length(length(y0)), y1)), y2)))) -> c9(MARK(length(and(s(and(length(length(y0)), y1)), y2)))) MARK(length(length(and(s(and(length(cons(y0, y1)), y2)), y3)))) -> c9(MARK(length(and(s(and(length(cons(y0, y1)), y2)), y3)))) MARK(length(length(and(s(and(length(s(y0)), y1)), y2)))) -> c9(MARK(length(and(s(and(length(s(y0)), y1)), y2)))) MARK(length(length(and(s(and(length(y0), y1)), y2)))) -> c9(MARK(length(and(s(and(length(y0), y1)), y2)))) MARK(length(length(and(s(and(and(zeros, y0), y1)), y2)))) -> c9(MARK(length(and(s(and(and(zeros, y0), y1)), y2)))) MARK(length(length(and(s(length(and(and(y0, y1), y2))), y3)))) -> c9(MARK(length(and(s(length(and(and(y0, y1), 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-> c9(MARK(length(and(s(length(length(length(y0)))), y1)))) MARK(length(length(and(s(length(length(cons(y0, y1)))), y2)))) -> c9(MARK(length(and(s(length(length(cons(y0, y1)))), y2)))) MARK(length(length(and(s(length(length(s(y0)))), y1)))) -> c9(MARK(length(and(s(length(length(s(y0)))), y1)))) MARK(length(length(and(s(length(length(y0))), y1)))) -> c9(MARK(length(and(s(length(length(y0))), y1)))) MARK(length(length(and(s(length(zeros)), y0)))) -> c9(MARK(length(and(s(length(zeros)), y0)))) MARK(length(length(and(s(cons(cons(y0, y1), y2)), y3)))) -> c9(MARK(length(and(s(cons(cons(y0, y1), y2)), y3)))) MARK(length(length(and(s(cons(s(y0), y1)), y2)))) -> c9(MARK(length(and(s(cons(s(y0), y1)), y2)))) MARK(length(length(and(s(cons(and(cons(y0, y1), y2), y3)), y4)))) -> c9(MARK(length(and(s(cons(and(cons(y0, y1), y2), y3)), y4)))) MARK(length(length(and(s(cons(and(tt, y0), y1)), y2)))) -> c9(MARK(length(and(s(cons(and(tt, y0), y1)), y2)))) MARK(length(length(and(s(cons(and(s(y0), y1), 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c9(MARK(length(and(length(s(cons(and(length(length(y0)), y1), y2))), y3)))) MARK(length(length(and(length(s(cons(and(length(cons(y0, y1)), y2), y3))), y4)))) -> c9(MARK(length(and(length(s(cons(and(length(cons(y0, y1)), y2), y3))), y4)))) MARK(length(length(and(length(s(cons(and(length(s(y0)), y1), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(and(length(s(y0)), y1), y2))), y3)))) MARK(length(length(and(length(s(cons(and(length(y0), y1), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(and(length(y0), y1), y2))), y3)))) MARK(length(length(and(length(s(cons(and(and(zeros, y0), y1), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(and(and(zeros, y0), y1), y2))), y3)))) MARK(length(length(and(length(s(cons(length(and(and(y0, y1), y2)), y3))), y4)))) -> c9(MARK(length(and(length(s(cons(length(and(and(y0, y1), y2)), y3))), y4)))) MARK(length(length(and(length(s(cons(length(and(length(y0), y1)), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(length(and(length(y0), y1)), y2))), y3)))) MARK(length(length(and(length(s(cons(length(and(cons(y0, y1), y2)), y3))), y4)))) -> c9(MARK(length(and(length(s(cons(length(and(cons(y0, y1), y2)), y3))), y4)))) MARK(length(length(and(length(s(cons(length(and(tt, y0)), y1))), y2)))) -> c9(MARK(length(and(length(s(cons(length(and(tt, y0)), y1))), y2)))) MARK(length(length(and(length(s(cons(length(and(s(y0), y1)), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(length(and(s(y0), y1)), y2))), y3)))) MARK(length(length(and(length(s(cons(length(and(y0, y1)), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(length(and(y0, y1)), y2))), y3)))) MARK(length(length(and(length(s(cons(length(and(zeros, y0)), y1))), y2)))) -> c9(MARK(length(and(length(s(cons(length(and(zeros, y0)), y1))), y2)))) MARK(length(length(and(length(s(cons(length(length(zeros)), y0))), y1)))) -> c9(MARK(length(and(length(s(cons(length(length(zeros)), y0))), y1)))) MARK(length(length(and(length(s(cons(length(length(and(y0, y1))), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(length(length(and(y0, y1))), y2))), y3)))) MARK(length(length(and(length(s(cons(length(length(length(y0))), y1))), y2)))) -> c9(MARK(length(and(length(s(cons(length(length(length(y0))), y1))), y2)))) MARK(length(length(and(length(s(cons(length(length(cons(y0, y1))), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(length(length(cons(y0, y1))), y2))), y3)))) MARK(length(length(and(length(s(cons(length(length(s(y0))), y1))), y2)))) -> c9(MARK(length(and(length(s(cons(length(length(s(y0))), y1))), y2)))) MARK(length(length(and(length(s(cons(length(length(y0)), y1))), y2)))) -> c9(MARK(length(and(length(s(cons(length(length(y0)), y1))), y2)))) MARK(length(length(and(length(s(cons(length(zeros), y0))), y1)))) -> c9(MARK(length(and(length(s(cons(length(zeros), y0))), y1)))) S tuples: A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(cons(z0, z1))) -> c9(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c8(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c8(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c8(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c8(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(length(zeros), x1)) -> c8(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c8(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c8(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(cons(z0, z1)), x1)) -> c8(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c8(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c8(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c9(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c9(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(cons(z0, z1), x1))) -> c9(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c9(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c9(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(zeros, x1))) -> c9(A__LENGTH(a__and(a__zeros, x1))) MARK(length(length(zeros))) -> c9(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c9(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c9(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(cons(z0, z1)))) -> c9(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c9(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(zeros)) -> c9(A__LENGTH(cons(0, zeros))) A__AND(tt, cons(y0, y1)) -> c2(MARK(cons(y0, y1))) A__AND(tt, s(y0)) -> c2(MARK(s(y0))) A__AND(tt, and(cons(y0, y1), y2)) -> c2(MARK(and(cons(y0, y1), y2))) A__AND(tt, and(tt, y0)) -> c2(MARK(and(tt, y0))) A__AND(tt, and(s(y0), y1)) -> c2(MARK(and(s(y0), y1))) A__AND(tt, length(cons(y0, y1))) -> c2(MARK(length(cons(y0, y1)))) A__AND(tt, length(s(y0))) -> c2(MARK(length(s(y0)))) A__AND(tt, and(and(and(y0, y1), y2), y3)) -> c2(MARK(and(and(and(y0, y1), y2), y3))) A__AND(tt, and(and(length(y0), y1), y2)) -> c2(MARK(and(and(length(y0), y1), y2))) A__AND(tt, and(and(cons(y0, y1), y2), y3)) -> c2(MARK(and(and(cons(y0, y1), y2), y3))) A__AND(tt, and(and(tt, y0), y1)) -> c2(MARK(and(and(tt, y0), y1))) A__AND(tt, and(and(s(y0), y1), y2)) -> c2(MARK(and(and(s(y0), y1), y2))) A__AND(tt, and(and(y0, y1), y2)) -> c2(MARK(and(and(y0, y1), y2))) A__AND(tt, and(length(zeros), y0)) -> c2(MARK(and(length(zeros), y0))) A__AND(tt, and(length(and(y0, y1)), y2)) -> c2(MARK(and(length(and(y0, y1)), y2))) A__AND(tt, and(length(length(y0)), y1)) -> c2(MARK(and(length(length(y0)), y1))) A__AND(tt, and(length(cons(y0, y1)), y2)) -> c2(MARK(and(length(cons(y0, y1)), y2))) A__AND(tt, and(length(s(y0)), y1)) -> c2(MARK(and(length(s(y0)), y1))) A__AND(tt, and(length(y0), y1)) -> c2(MARK(and(length(y0), y1))) A__AND(tt, and(and(zeros, y0), y1)) -> c2(MARK(and(and(zeros, y0), y1))) A__AND(tt, length(and(and(y0, y1), y2))) -> c2(MARK(length(and(and(y0, y1), y2)))) A__AND(tt, length(and(length(y0), y1))) -> c2(MARK(length(and(length(y0), y1)))) A__AND(tt, length(and(cons(y0, y1), y2))) -> c2(MARK(length(and(cons(y0, y1), y2)))) A__AND(tt, length(and(tt, y0))) -> c2(MARK(length(and(tt, y0)))) A__AND(tt, length(and(s(y0), y1))) -> c2(MARK(length(and(s(y0), y1)))) A__AND(tt, length(and(y0, y1))) -> c2(MARK(length(and(y0, y1)))) A__AND(tt, length(and(zeros, y0))) -> c2(MARK(length(and(zeros, y0)))) A__AND(tt, length(length(zeros))) -> c2(MARK(length(length(zeros)))) A__AND(tt, length(length(and(y0, y1)))) -> c2(MARK(length(length(and(y0, y1))))) A__AND(tt, length(length(length(y0)))) -> c2(MARK(length(length(length(y0))))) A__AND(tt, length(length(cons(y0, y1)))) -> c2(MARK(length(length(cons(y0, y1))))) A__AND(tt, length(length(s(y0)))) -> c2(MARK(length(length(s(y0))))) A__AND(tt, length(length(y0))) -> c2(MARK(length(length(y0)))) A__AND(tt, length(zeros)) -> c2(MARK(length(zeros))) MARK(cons(cons(y0, y1), z1)) -> c10(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c10(MARK(s(y0))) MARK(cons(and(cons(y0, y1), y2), z1)) -> c10(MARK(and(cons(y0, y1), y2))) MARK(cons(and(tt, y0), z1)) -> c10(MARK(and(tt, y0))) MARK(cons(and(s(y0), y1), z1)) -> c10(MARK(and(s(y0), y1))) MARK(cons(length(cons(y0, y1)), z1)) -> c10(MARK(length(cons(y0, y1)))) MARK(cons(length(s(y0)), z1)) -> c10(MARK(length(s(y0)))) MARK(cons(and(and(and(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(and(y0, y1), y2), y3))) MARK(cons(and(and(length(y0), y1), y2), z1)) -> c10(MARK(and(and(length(y0), y1), y2))) MARK(cons(and(and(cons(y0, y1), y2), y3), z1)) -> c10(MARK(and(and(cons(y0, y1), y2), y3))) MARK(cons(and(and(tt, y0), y1), z1)) -> c10(MARK(and(and(tt, y0), y1))) MARK(cons(and(and(s(y0), y1), y2), z1)) -> c10(MARK(and(and(s(y0), y1), y2))) MARK(cons(and(and(y0, y1), y2), z1)) -> c10(MARK(and(and(y0, y1), y2))) MARK(cons(and(length(zeros), y0), z1)) -> c10(MARK(and(length(zeros), y0))) MARK(cons(and(length(and(y0, y1)), y2), z1)) -> c10(MARK(and(length(and(y0, y1)), y2))) MARK(cons(and(length(length(y0)), y1), z1)) -> c10(MARK(and(length(length(y0)), y1))) MARK(cons(and(length(cons(y0, y1)), y2), z1)) -> c10(MARK(and(length(cons(y0, y1)), y2))) MARK(cons(and(length(s(y0)), y1), z1)) -> c10(MARK(and(length(s(y0)), y1))) MARK(cons(and(length(y0), y1), z1)) -> c10(MARK(and(length(y0), y1))) MARK(cons(and(and(zeros, y0), y1), z1)) -> c10(MARK(and(and(zeros, y0), y1))) MARK(cons(length(and(and(y0, y1), y2)), z1)) -> c10(MARK(length(and(and(y0, y1), y2)))) MARK(cons(length(and(length(y0), y1)), z1)) -> c10(MARK(length(and(length(y0), y1)))) MARK(cons(length(and(cons(y0, y1), y2)), z1)) -> c10(MARK(length(and(cons(y0, y1), y2)))) MARK(cons(length(and(tt, y0)), z1)) -> c10(MARK(length(and(tt, y0)))) MARK(cons(length(and(s(y0), y1)), z1)) -> c10(MARK(length(and(s(y0), y1)))) MARK(cons(length(and(y0, y1)), z1)) -> c10(MARK(length(and(y0, y1)))) MARK(cons(length(and(zeros, y0)), z1)) -> c10(MARK(length(and(zeros, y0)))) MARK(cons(length(length(zeros)), z1)) -> c10(MARK(length(length(zeros)))) MARK(cons(length(length(and(y0, y1))), z1)) -> c10(MARK(length(length(and(y0, y1))))) MARK(cons(length(length(length(y0))), z1)) -> c10(MARK(length(length(length(y0))))) MARK(cons(length(length(cons(y0, y1))), z1)) -> c10(MARK(length(length(cons(y0, y1))))) MARK(cons(length(length(s(y0))), z1)) -> c10(MARK(length(length(s(y0))))) MARK(cons(length(length(y0)), z1)) -> c10(MARK(length(length(y0)))) MARK(cons(length(zeros), z1)) -> c10(MARK(length(zeros))) MARK(s(s(y0))) -> c14(MARK(s(y0))) MARK(s(and(cons(y0, y1), y2))) -> c14(MARK(and(cons(y0, y1), y2))) MARK(s(and(tt, y0))) -> c14(MARK(and(tt, y0))) MARK(s(and(s(y0), y1))) -> c14(MARK(and(s(y0), y1))) MARK(s(length(cons(y0, y1)))) -> c14(MARK(length(cons(y0, y1)))) MARK(s(length(s(y0)))) -> c14(MARK(length(s(y0)))) MARK(s(and(and(and(y0, y1), y2), y3))) -> c14(MARK(and(and(and(y0, y1), y2), y3))) MARK(s(and(and(length(y0), y1), y2))) -> c14(MARK(and(and(length(y0), y1), y2))) MARK(s(and(and(cons(y0, y1), y2), y3))) -> c14(MARK(and(and(cons(y0, y1), y2), y3))) MARK(s(and(and(tt, y0), y1))) -> c14(MARK(and(and(tt, y0), y1))) MARK(s(and(and(s(y0), y1), y2))) -> c14(MARK(and(and(s(y0), y1), y2))) MARK(s(and(and(y0, y1), y2))) -> c14(MARK(and(and(y0, y1), y2))) MARK(s(and(length(zeros), y0))) -> c14(MARK(and(length(zeros), y0))) MARK(s(and(length(and(y0, y1)), y2))) -> c14(MARK(and(length(and(y0, y1)), y2))) MARK(s(and(length(length(y0)), y1))) -> c14(MARK(and(length(length(y0)), y1))) MARK(s(and(length(cons(y0, y1)), y2))) -> c14(MARK(and(length(cons(y0, y1)), y2))) MARK(s(and(length(s(y0)), y1))) -> c14(MARK(and(length(s(y0)), y1))) MARK(s(and(length(y0), y1))) -> c14(MARK(and(length(y0), y1))) MARK(s(and(and(zeros, y0), y1))) -> c14(MARK(and(and(zeros, y0), y1))) MARK(s(length(and(and(y0, y1), y2)))) -> c14(MARK(length(and(and(y0, y1), y2)))) MARK(s(length(and(length(y0), y1)))) -> c14(MARK(length(and(length(y0), y1)))) MARK(s(length(and(cons(y0, y1), y2)))) -> 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c5(MARK(and(cons(length(cons(y0, y1)), y2), z2))) A__LENGTH(cons(z0, and(cons(length(s(y0)), y1), z2))) -> c5(MARK(and(cons(length(s(y0)), y1), z2))) A__LENGTH(cons(z0, and(cons(and(and(and(y0, y1), y2), y3), y4), z2))) -> c5(MARK(and(cons(and(and(and(y0, y1), y2), y3), y4), z2))) A__LENGTH(cons(z0, and(cons(and(and(length(y0), y1), y2), y3), z2))) -> c5(MARK(and(cons(and(and(length(y0), y1), y2), y3), z2))) A__LENGTH(cons(z0, and(cons(and(and(cons(y0, y1), y2), y3), y4), z2))) -> c5(MARK(and(cons(and(and(cons(y0, y1), y2), y3), y4), z2))) A__LENGTH(cons(z0, and(cons(and(and(tt, y0), y1), y2), z2))) -> c5(MARK(and(cons(and(and(tt, y0), y1), y2), z2))) A__LENGTH(cons(z0, and(cons(and(and(s(y0), y1), y2), y3), z2))) -> c5(MARK(and(cons(and(and(s(y0), y1), y2), y3), z2))) A__LENGTH(cons(z0, and(cons(and(and(y0, y1), y2), y3), z2))) -> c5(MARK(and(cons(and(and(y0, y1), y2), y3), z2))) A__LENGTH(cons(z0, and(cons(and(length(zeros), y0), y1), z2))) -> c5(MARK(and(cons(and(length(zeros), y0), 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y2), z2))) A__LENGTH(cons(z0, and(cons(length(and(cons(y0, y1), y2)), y3), z2))) -> c5(MARK(and(cons(length(and(cons(y0, y1), y2)), y3), z2))) A__LENGTH(cons(z0, and(cons(length(and(tt, y0)), y1), z2))) -> c5(MARK(and(cons(length(and(tt, y0)), y1), z2))) A__LENGTH(cons(z0, and(cons(length(and(s(y0), y1)), y2), z2))) -> c5(MARK(and(cons(length(and(s(y0), y1)), y2), z2))) A__LENGTH(cons(z0, and(cons(length(and(y0, y1)), y2), z2))) -> c5(MARK(and(cons(length(and(y0, y1)), y2), z2))) A__LENGTH(cons(z0, and(cons(length(and(zeros, y0)), y1), z2))) -> c5(MARK(and(cons(length(and(zeros, y0)), y1), z2))) A__LENGTH(cons(z0, and(cons(length(length(zeros)), y0), z2))) -> c5(MARK(and(cons(length(length(zeros)), y0), z2))) A__LENGTH(cons(z0, and(cons(length(length(and(y0, y1))), y2), z2))) -> c5(MARK(and(cons(length(length(and(y0, y1))), y2), z2))) A__LENGTH(cons(z0, and(cons(length(length(length(y0))), y1), z2))) -> c5(MARK(and(cons(length(length(length(y0))), y1), z2))) A__LENGTH(cons(z0, 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length(s(y0))))) A__LENGTH(cons(z0, and(tt, and(and(and(y0, y1), y2), y3)))) -> c5(MARK(and(tt, and(and(and(y0, y1), y2), y3)))) A__LENGTH(cons(z0, and(tt, and(and(length(y0), y1), y2)))) -> c5(MARK(and(tt, and(and(length(y0), y1), y2)))) A__LENGTH(cons(z0, and(tt, and(and(cons(y0, y1), y2), y3)))) -> c5(MARK(and(tt, and(and(cons(y0, y1), y2), y3)))) A__LENGTH(cons(z0, and(tt, and(and(tt, y0), y1)))) -> c5(MARK(and(tt, and(and(tt, y0), y1)))) A__LENGTH(cons(z0, and(tt, and(and(s(y0), y1), y2)))) -> c5(MARK(and(tt, and(and(s(y0), y1), y2)))) A__LENGTH(cons(z0, and(tt, and(and(y0, y1), y2)))) -> c5(MARK(and(tt, and(and(y0, y1), y2)))) A__LENGTH(cons(z0, and(tt, and(length(zeros), y0)))) -> c5(MARK(and(tt, and(length(zeros), y0)))) A__LENGTH(cons(z0, and(tt, and(length(and(y0, y1)), y2)))) -> c5(MARK(and(tt, and(length(and(y0, y1)), y2)))) A__LENGTH(cons(z0, and(tt, and(length(length(y0)), y1)))) -> c5(MARK(and(tt, and(length(length(y0)), y1)))) A__LENGTH(cons(z0, and(tt, and(length(cons(y0, y1)), y2)))) -> c5(MARK(and(tt, and(length(cons(y0, y1)), y2)))) A__LENGTH(cons(z0, and(tt, and(length(s(y0)), y1)))) -> c5(MARK(and(tt, and(length(s(y0)), y1)))) A__LENGTH(cons(z0, and(tt, and(length(y0), y1)))) -> c5(MARK(and(tt, and(length(y0), y1)))) A__LENGTH(cons(z0, and(tt, and(and(zeros, y0), y1)))) -> c5(MARK(and(tt, and(and(zeros, y0), y1)))) A__LENGTH(cons(z0, and(tt, length(and(and(y0, y1), y2))))) -> c5(MARK(and(tt, length(and(and(y0, y1), y2))))) A__LENGTH(cons(z0, and(tt, length(and(length(y0), y1))))) -> c5(MARK(and(tt, length(and(length(y0), y1))))) A__LENGTH(cons(z0, and(tt, length(and(cons(y0, y1), y2))))) -> c5(MARK(and(tt, length(and(cons(y0, y1), y2))))) A__LENGTH(cons(z0, and(tt, length(and(tt, y0))))) -> c5(MARK(and(tt, length(and(tt, y0))))) A__LENGTH(cons(z0, and(tt, length(and(s(y0), y1))))) -> c5(MARK(and(tt, length(and(s(y0), y1))))) A__LENGTH(cons(z0, and(tt, length(and(y0, y1))))) -> c5(MARK(and(tt, length(and(y0, y1))))) A__LENGTH(cons(z0, and(tt, length(and(zeros, y0))))) -> c5(MARK(and(tt, length(and(zeros, y0))))) A__LENGTH(cons(z0, and(tt, length(length(zeros))))) -> c5(MARK(and(tt, length(length(zeros))))) A__LENGTH(cons(z0, and(tt, length(length(and(y0, y1)))))) -> c5(MARK(and(tt, length(length(and(y0, y1)))))) A__LENGTH(cons(z0, and(tt, length(length(length(y0)))))) -> c5(MARK(and(tt, length(length(length(y0)))))) A__LENGTH(cons(z0, and(tt, length(length(cons(y0, y1)))))) -> c5(MARK(and(tt, length(length(cons(y0, y1)))))) A__LENGTH(cons(z0, and(tt, length(length(s(y0)))))) -> c5(MARK(and(tt, length(length(s(y0)))))) A__LENGTH(cons(z0, and(tt, length(length(y0))))) -> c5(MARK(and(tt, length(length(y0))))) A__LENGTH(cons(z0, and(tt, length(zeros)))) -> c5(MARK(and(tt, length(zeros)))) A__LENGTH(cons(z0, and(s(s(y0)), z2))) -> c5(MARK(and(s(s(y0)), z2))) A__LENGTH(cons(z0, and(s(and(cons(y0, y1), y2)), z2))) -> c5(MARK(and(s(and(cons(y0, y1), y2)), z2))) A__LENGTH(cons(z0, and(s(and(tt, y0)), z2))) -> c5(MARK(and(s(and(tt, y0)), z2))) A__LENGTH(cons(z0, and(s(and(s(y0), y1)), z2))) -> c5(MARK(and(s(and(s(y0), y1)), z2))) A__LENGTH(cons(z0, and(s(length(cons(y0, y1))), z2))) -> c5(MARK(and(s(length(cons(y0, y1))), z2))) A__LENGTH(cons(z0, and(s(length(s(y0))), z2))) -> c5(MARK(and(s(length(s(y0))), z2))) A__LENGTH(cons(z0, and(s(and(and(and(y0, y1), y2), y3)), z2))) -> c5(MARK(and(s(and(and(and(y0, y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(and(and(length(y0), y1), y2)), z2))) -> c5(MARK(and(s(and(and(length(y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(and(and(cons(y0, y1), y2), y3)), z2))) -> c5(MARK(and(s(and(and(cons(y0, y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(and(and(tt, y0), y1)), z2))) -> c5(MARK(and(s(and(and(tt, y0), y1)), z2))) A__LENGTH(cons(z0, and(s(and(and(s(y0), y1), y2)), z2))) -> c5(MARK(and(s(and(and(s(y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(and(and(y0, y1), y2)), z2))) -> c5(MARK(and(s(and(and(y0, y1), y2)), z2))) A__LENGTH(cons(z0, 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z2))) -> c5(MARK(and(s(length(length(s(y0)))), z2))) A__LENGTH(cons(z0, and(s(length(length(y0))), z2))) -> c5(MARK(and(s(length(length(y0))), z2))) A__LENGTH(cons(z0, and(s(length(zeros)), z2))) -> c5(MARK(and(s(length(zeros)), z2))) A__LENGTH(cons(z0, and(s(cons(cons(y0, y1), y2)), z2))) -> c5(MARK(and(s(cons(cons(y0, y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(s(y0), y1)), z2))) -> c5(MARK(and(s(cons(s(y0), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(and(cons(y0, y1), y2), y3)), z2))) -> c5(MARK(and(s(cons(and(cons(y0, y1), y2), y3)), z2))) A__LENGTH(cons(z0, and(s(cons(and(tt, y0), y1)), z2))) -> c5(MARK(and(s(cons(and(tt, y0), y1)), z2))) A__LENGTH(cons(z0, and(s(cons(and(s(y0), y1), y2)), z2))) -> c5(MARK(and(s(cons(and(s(y0), y1), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(cons(y0, y1)), y2)), z2))) -> c5(MARK(and(s(cons(length(cons(y0, y1)), y2)), z2))) A__LENGTH(cons(z0, and(s(cons(length(s(y0)), y1)), z2))) -> c5(MARK(and(s(cons(length(s(y0)), y1)), z2))) 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c5(MARK(length(s(cons(and(length(length(y0)), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(and(length(cons(y0, y1)), y2), y3))))) -> c5(MARK(length(s(cons(and(length(cons(y0, y1)), y2), y3))))) A__LENGTH(cons(z0, length(s(cons(and(length(s(y0)), y1), y2))))) -> c5(MARK(length(s(cons(and(length(s(y0)), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(and(length(y0), y1), y2))))) -> c5(MARK(length(s(cons(and(length(y0), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(and(and(zeros, y0), y1), y2))))) -> c5(MARK(length(s(cons(and(and(zeros, y0), y1), y2))))) A__LENGTH(cons(z0, length(s(cons(length(and(and(y0, y1), y2)), y3))))) -> c5(MARK(length(s(cons(length(and(and(y0, y1), y2)), y3))))) A__LENGTH(cons(z0, length(s(cons(length(and(length(y0), y1)), y2))))) -> c5(MARK(length(s(cons(length(and(length(y0), y1)), y2))))) A__LENGTH(cons(z0, length(s(cons(length(and(cons(y0, y1), y2)), y3))))) -> c5(MARK(length(s(cons(length(and(cons(y0, y1), y2)), y3))))) A__LENGTH(cons(z0, 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z2)) -> c8(MARK(and(length(length(y0)), z1))) MARK(and(and(length(cons(y0, y1)), z1), z2)) -> c8(MARK(and(length(cons(y0, y1)), z1))) MARK(and(and(length(s(y0)), z1), z2)) -> c8(MARK(and(length(s(y0)), z1))) MARK(and(and(length(y0), z1), z2)) -> c8(MARK(and(length(y0), z1))) MARK(and(and(and(zeros, y0), z1), z2)) -> c8(MARK(and(and(zeros, y0), z1))) MARK(and(and(cons(cons(y0, y1), y2), z1), z2)) -> c8(MARK(and(cons(cons(y0, y1), y2), z1))) MARK(and(and(cons(s(y0), y1), z1), z2)) -> c8(MARK(and(cons(s(y0), y1), z1))) MARK(and(and(cons(and(cons(y0, y1), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(cons(y0, y1), y2), y3), z1))) MARK(and(and(cons(and(tt, y0), y1), z1), z2)) -> c8(MARK(and(cons(and(tt, y0), y1), z1))) MARK(and(and(cons(and(s(y0), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(s(y0), y1), y2), z1))) MARK(and(and(cons(length(cons(y0, y1)), y2), z1), z2)) -> c8(MARK(and(cons(length(cons(y0, y1)), y2), z1))) MARK(and(and(cons(length(s(y0)), y1), z1), z2)) -> c8(MARK(and(cons(length(s(y0)), y1), z1))) MARK(and(and(cons(and(and(and(y0, y1), y2), y3), y4), z1), z2)) -> c8(MARK(and(cons(and(and(and(y0, y1), y2), y3), y4), z1))) MARK(and(and(cons(and(and(length(y0), y1), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(and(length(y0), y1), y2), y3), z1))) MARK(and(and(cons(and(and(cons(y0, y1), y2), y3), y4), z1), z2)) -> c8(MARK(and(cons(and(and(cons(y0, y1), y2), y3), y4), z1))) MARK(and(and(cons(and(and(tt, y0), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(and(tt, y0), y1), y2), z1))) MARK(and(and(cons(and(and(s(y0), y1), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(and(s(y0), y1), y2), y3), z1))) MARK(and(and(cons(and(and(y0, y1), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(and(y0, y1), y2), y3), z1))) MARK(and(and(cons(and(length(zeros), y0), y1), z1), z2)) -> c8(MARK(and(cons(and(length(zeros), y0), y1), z1))) MARK(and(and(cons(and(length(and(y0, y1)), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(length(and(y0, y1)), y2), y3), z1))) MARK(and(and(cons(and(length(length(y0)), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(length(length(y0)), y1), y2), z1))) MARK(and(and(cons(and(length(cons(y0, y1)), y2), y3), z1), z2)) -> c8(MARK(and(cons(and(length(cons(y0, y1)), y2), y3), z1))) MARK(and(and(cons(and(length(s(y0)), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(length(s(y0)), y1), y2), z1))) MARK(and(and(cons(and(length(y0), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(length(y0), y1), y2), z1))) MARK(and(and(cons(and(and(zeros, y0), y1), y2), z1), z2)) -> c8(MARK(and(cons(and(and(zeros, y0), y1), y2), z1))) MARK(and(and(cons(length(and(and(y0, y1), y2)), y3), z1), z2)) -> c8(MARK(and(cons(length(and(and(y0, y1), y2)), y3), z1))) MARK(and(and(cons(length(and(length(y0), y1)), y2), z1), z2)) -> c8(MARK(and(cons(length(and(length(y0), y1)), y2), z1))) MARK(and(and(cons(length(and(cons(y0, y1), y2)), y3), z1), z2)) -> c8(MARK(and(cons(length(and(cons(y0, y1), y2)), y3), z1))) MARK(and(and(cons(length(and(tt, y0)), y1), z1), 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c9(MARK(and(and(s(and(and(length(y0), y1), y2)), y3), z1))) MARK(length(and(and(s(and(and(cons(y0, y1), y2), y3)), y4), z1))) -> c9(MARK(and(and(s(and(and(cons(y0, y1), y2), y3)), y4), z1))) MARK(length(and(and(s(and(and(tt, y0), y1)), y2), z1))) -> c9(MARK(and(and(s(and(and(tt, y0), y1)), y2), z1))) MARK(length(and(and(s(and(and(s(y0), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(and(and(s(y0), y1), y2)), y3), z1))) MARK(length(and(and(s(and(and(y0, y1), y2)), y3), z1))) -> c9(MARK(and(and(s(and(and(y0, y1), y2)), y3), z1))) MARK(length(and(and(s(and(length(zeros), y0)), y1), z1))) -> c9(MARK(and(and(s(and(length(zeros), y0)), y1), z1))) MARK(length(and(and(s(and(length(and(y0, y1)), y2)), y3), z1))) -> c9(MARK(and(and(s(and(length(and(y0, y1)), y2)), y3), z1))) MARK(length(and(and(s(and(length(length(y0)), y1)), y2), z1))) -> c9(MARK(and(and(s(and(length(length(y0)), y1)), y2), z1))) MARK(length(and(and(s(and(length(cons(y0, y1)), y2)), y3), z1))) -> c9(MARK(and(and(s(and(length(cons(y0, y1)), y2)), y3), z1))) MARK(length(and(and(s(and(length(s(y0)), y1)), y2), z1))) -> c9(MARK(and(and(s(and(length(s(y0)), y1)), y2), z1))) MARK(length(and(and(s(and(length(y0), y1)), y2), z1))) -> c9(MARK(and(and(s(and(length(y0), y1)), y2), z1))) MARK(length(and(and(s(and(and(zeros, y0), y1)), y2), z1))) -> c9(MARK(and(and(s(and(and(zeros, y0), y1)), y2), z1))) MARK(length(and(and(s(length(and(and(y0, y1), y2))), y3), z1))) -> c9(MARK(and(and(s(length(and(and(y0, y1), y2))), y3), z1))) MARK(length(and(and(s(length(and(length(y0), y1))), y2), z1))) -> c9(MARK(and(and(s(length(and(length(y0), y1))), y2), z1))) MARK(length(and(and(s(length(and(cons(y0, y1), y2))), y3), z1))) -> c9(MARK(and(and(s(length(and(cons(y0, y1), y2))), y3), z1))) MARK(length(and(and(s(length(and(tt, y0))), y1), z1))) -> c9(MARK(and(and(s(length(and(tt, y0))), y1), z1))) MARK(length(and(and(s(length(and(s(y0), y1))), y2), z1))) -> c9(MARK(and(and(s(length(and(s(y0), y1))), y2), z1))) MARK(length(and(and(s(length(and(y0, y1))), y2), z1))) -> c9(MARK(and(and(s(length(and(y0, y1))), y2), z1))) MARK(length(and(and(s(length(and(zeros, y0))), y1), z1))) -> c9(MARK(and(and(s(length(and(zeros, y0))), y1), z1))) MARK(length(and(and(s(length(length(zeros))), y0), z1))) -> c9(MARK(and(and(s(length(length(zeros))), y0), z1))) MARK(length(and(and(s(length(length(and(y0, y1)))), y2), z1))) -> c9(MARK(and(and(s(length(length(and(y0, y1)))), y2), z1))) MARK(length(and(and(s(length(length(length(y0)))), y1), z1))) -> c9(MARK(and(and(s(length(length(length(y0)))), y1), z1))) MARK(length(and(and(s(length(length(cons(y0, y1)))), y2), z1))) -> c9(MARK(and(and(s(length(length(cons(y0, y1)))), y2), z1))) MARK(length(and(and(s(length(length(s(y0)))), y1), z1))) -> c9(MARK(and(and(s(length(length(s(y0)))), y1), z1))) MARK(length(and(and(s(length(length(y0))), y1), z1))) -> c9(MARK(and(and(s(length(length(y0))), y1), z1))) MARK(length(and(and(s(length(zeros)), y0), z1))) -> c9(MARK(and(and(s(length(zeros)), y0), z1))) MARK(length(and(and(s(cons(cons(y0, y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(cons(y0, y1), y2)), y3), z1))) MARK(length(and(and(s(cons(s(y0), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(s(y0), y1)), y2), z1))) MARK(length(and(and(s(cons(and(cons(y0, y1), y2), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(and(cons(y0, y1), y2), y3)), y4), z1))) MARK(length(and(and(s(cons(and(tt, y0), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(and(tt, y0), y1)), y2), z1))) MARK(length(and(and(s(cons(and(s(y0), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(and(s(y0), y1), y2)), y3), z1))) MARK(length(and(and(s(cons(length(cons(y0, y1)), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(length(cons(y0, y1)), y2)), y3), z1))) MARK(length(and(and(s(cons(length(s(y0)), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(length(s(y0)), y1)), y2), z1))) MARK(length(and(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), y5), z1))) -> c9(MARK(and(and(s(cons(and(and(and(y0, y1), y2), y3), y4)), y5), z1))) MARK(length(and(and(s(cons(and(and(length(y0), y1), y2), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(and(and(length(y0), y1), y2), y3)), y4), z1))) MARK(length(and(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), y5), z1))) -> c9(MARK(and(and(s(cons(and(and(cons(y0, y1), y2), y3), y4)), y5), z1))) MARK(length(and(and(s(cons(and(and(tt, y0), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(and(and(tt, y0), y1), y2)), y3), z1))) MARK(length(and(and(s(cons(and(and(s(y0), y1), y2), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(and(and(s(y0), y1), y2), y3)), y4), z1))) MARK(length(and(and(s(cons(and(and(y0, y1), y2), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(and(and(y0, y1), y2), y3)), y4), z1))) MARK(length(and(and(s(cons(and(length(zeros), y0), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(and(length(zeros), y0), y1)), y2), z1))) MARK(length(and(and(s(cons(and(length(and(y0, y1)), y2), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(and(length(and(y0, y1)), y2), y3)), y4), z1))) MARK(length(and(and(s(cons(and(length(length(y0)), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(and(length(length(y0)), y1), y2)), y3), z1))) MARK(length(and(and(s(cons(and(length(cons(y0, y1)), y2), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(and(length(cons(y0, y1)), y2), y3)), y4), z1))) MARK(length(and(and(s(cons(and(length(s(y0)), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(and(length(s(y0)), y1), y2)), y3), z1))) MARK(length(and(and(s(cons(and(length(y0), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(and(length(y0), y1), y2)), y3), z1))) MARK(length(and(and(s(cons(and(and(zeros, y0), y1), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(and(and(zeros, y0), y1), y2)), y3), z1))) MARK(length(and(and(s(cons(length(and(and(y0, y1), y2)), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(length(and(and(y0, y1), y2)), y3)), y4), z1))) MARK(length(and(and(s(cons(length(and(length(y0), y1)), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(length(and(length(y0), y1)), y2)), y3), z1))) MARK(length(and(and(s(cons(length(and(cons(y0, y1), y2)), y3)), y4), z1))) -> c9(MARK(and(and(s(cons(length(and(cons(y0, y1), y2)), y3)), y4), z1))) MARK(length(and(and(s(cons(length(and(tt, y0)), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(length(and(tt, y0)), y1)), y2), z1))) MARK(length(and(and(s(cons(length(and(s(y0), y1)), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(length(and(s(y0), y1)), y2)), y3), z1))) MARK(length(and(and(s(cons(length(and(y0, y1)), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(length(and(y0, y1)), y2)), y3), z1))) MARK(length(and(and(s(cons(length(and(zeros, y0)), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(length(and(zeros, y0)), y1)), y2), z1))) MARK(length(and(and(s(cons(length(length(zeros)), y0)), y1), z1))) -> c9(MARK(and(and(s(cons(length(length(zeros)), y0)), y1), z1))) MARK(length(and(and(s(cons(length(length(and(y0, y1))), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(length(length(and(y0, y1))), y2)), y3), z1))) MARK(length(and(and(s(cons(length(length(length(y0))), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(length(length(length(y0))), y1)), y2), z1))) MARK(length(and(and(s(cons(length(length(cons(y0, y1))), y2)), y3), z1))) -> c9(MARK(and(and(s(cons(length(length(cons(y0, y1))), y2)), y3), z1))) MARK(length(and(and(s(cons(length(length(s(y0))), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(length(length(s(y0))), y1)), y2), z1))) MARK(length(and(and(s(cons(length(length(y0)), y1)), y2), z1))) -> c9(MARK(and(and(s(cons(length(length(y0)), y1)), y2), z1))) MARK(length(and(and(s(cons(length(zeros), y0)), y1), z1))) -> c9(MARK(and(and(s(cons(length(zeros), y0)), y1), z1))) MARK(length(and(length(and(and(y0, y1), y2)), z1))) -> c9(MARK(and(length(and(and(y0, y1), y2)), z1))) MARK(length(and(length(and(length(y0), y1)), z1))) -> c9(MARK(and(length(and(length(y0), y1)), z1))) MARK(length(and(length(and(cons(y0, y1), y2)), z1))) -> c9(MARK(and(length(and(cons(y0, y1), y2)), z1))) MARK(length(and(length(and(tt, y0)), z1))) -> c9(MARK(and(length(and(tt, y0)), z1))) MARK(length(and(length(and(s(y0), y1)), z1))) -> c9(MARK(and(length(and(s(y0), y1)), z1))) MARK(length(and(length(and(zeros, y0)), z1))) -> c9(MARK(and(length(and(zeros, y0)), z1))) MARK(length(and(length(length(zeros)), z1))) -> c9(MARK(and(length(length(zeros)), z1))) MARK(length(and(length(length(and(y0, y1))), z1))) -> c9(MARK(and(length(length(and(y0, y1))), z1))) MARK(length(and(length(length(length(y0))), z1))) -> c9(MARK(and(length(length(length(y0))), z1))) MARK(length(and(length(length(cons(y0, y1))), z1))) -> c9(MARK(and(length(length(cons(y0, y1))), z1))) MARK(length(and(length(length(s(y0))), z1))) -> c9(MARK(and(length(length(s(y0))), z1))) MARK(length(and(length(s(s(y0))), z1))) -> c9(MARK(and(length(s(s(y0))), z1))) MARK(length(and(length(s(and(cons(y0, y1), y2))), z1))) -> c9(MARK(and(length(s(and(cons(y0, y1), y2))), z1))) MARK(length(and(length(s(and(tt, y0))), z1))) -> c9(MARK(and(length(s(and(tt, y0))), z1))) MARK(length(and(length(s(and(s(y0), y1))), z1))) -> c9(MARK(and(length(s(and(s(y0), y1))), z1))) MARK(length(and(length(s(length(cons(y0, y1)))), z1))) -> c9(MARK(and(length(s(length(cons(y0, y1)))), z1))) MARK(length(and(length(s(length(s(y0)))), z1))) -> c9(MARK(and(length(s(length(s(y0)))), z1))) MARK(length(and(length(s(and(and(and(y0, y1), y2), y3))), z1))) -> c9(MARK(and(length(s(and(and(and(y0, y1), y2), y3))), z1))) MARK(length(and(length(s(and(and(length(y0), y1), y2))), z1))) -> c9(MARK(and(length(s(and(and(length(y0), y1), y2))), z1))) MARK(length(and(length(s(and(and(cons(y0, y1), y2), y3))), z1))) -> c9(MARK(and(length(s(and(and(cons(y0, y1), y2), y3))), z1))) MARK(length(and(length(s(and(and(tt, y0), y1))), z1))) -> c9(MARK(and(length(s(and(and(tt, y0), y1))), z1))) MARK(length(and(length(s(and(and(s(y0), y1), y2))), z1))) -> c9(MARK(and(length(s(and(and(s(y0), y1), y2))), z1))) MARK(length(and(length(s(and(and(y0, y1), y2))), z1))) -> c9(MARK(and(length(s(and(and(y0, y1), y2))), z1))) MARK(length(and(length(s(and(length(zeros), y0))), z1))) -> c9(MARK(and(length(s(and(length(zeros), y0))), z1))) MARK(length(and(length(s(and(length(and(y0, y1)), y2))), z1))) -> c9(MARK(and(length(s(and(length(and(y0, y1)), y2))), z1))) MARK(length(and(length(s(and(length(length(y0)), y1))), z1))) -> c9(MARK(and(length(s(and(length(length(y0)), y1))), z1))) MARK(length(and(length(s(and(length(cons(y0, y1)), y2))), z1))) -> c9(MARK(and(length(s(and(length(cons(y0, y1)), y2))), z1))) MARK(length(and(length(s(and(length(s(y0)), y1))), z1))) -> c9(MARK(and(length(s(and(length(s(y0)), y1))), z1))) MARK(length(and(length(s(and(length(y0), y1))), z1))) -> c9(MARK(and(length(s(and(length(y0), y1))), z1))) MARK(length(and(length(s(and(and(zeros, y0), y1))), z1))) -> c9(MARK(and(length(s(and(and(zeros, y0), y1))), z1))) MARK(length(and(length(s(length(and(and(y0, y1), y2)))), z1))) -> c9(MARK(and(length(s(length(and(and(y0, y1), y2)))), z1))) MARK(length(and(length(s(length(and(length(y0), y1)))), z1))) -> c9(MARK(and(length(s(length(and(length(y0), y1)))), z1))) MARK(length(and(length(s(length(and(cons(y0, y1), y2)))), z1))) -> c9(MARK(and(length(s(length(and(cons(y0, y1), y2)))), z1))) MARK(length(and(length(s(length(and(tt, y0)))), z1))) -> c9(MARK(and(length(s(length(and(tt, y0)))), z1))) MARK(length(and(length(s(length(and(s(y0), y1)))), z1))) -> c9(MARK(and(length(s(length(and(s(y0), y1)))), z1))) MARK(length(and(length(s(length(and(y0, y1)))), z1))) -> c9(MARK(and(length(s(length(and(y0, y1)))), z1))) MARK(length(and(length(s(length(and(zeros, y0)))), z1))) -> c9(MARK(and(length(s(length(and(zeros, y0)))), z1))) MARK(length(and(length(s(length(length(zeros)))), z1))) -> c9(MARK(and(length(s(length(length(zeros)))), z1))) MARK(length(and(length(s(length(length(and(y0, y1))))), z1))) -> c9(MARK(and(length(s(length(length(and(y0, y1))))), z1))) MARK(length(and(length(s(length(length(length(y0))))), z1))) -> c9(MARK(and(length(s(length(length(length(y0))))), z1))) MARK(length(and(length(s(length(length(cons(y0, y1))))), z1))) -> c9(MARK(and(length(s(length(length(cons(y0, y1))))), z1))) MARK(length(and(length(s(length(length(s(y0))))), z1))) -> c9(MARK(and(length(s(length(length(s(y0))))), z1))) MARK(length(and(length(s(length(length(y0)))), z1))) -> c9(MARK(and(length(s(length(length(y0)))), z1))) MARK(length(and(length(s(length(zeros))), z1))) -> c9(MARK(and(length(s(length(zeros))), z1))) MARK(length(and(length(s(cons(cons(y0, y1), y2))), z1))) -> c9(MARK(and(length(s(cons(cons(y0, y1), y2))), z1))) MARK(length(and(length(s(cons(s(y0), y1))), z1))) -> c9(MARK(and(length(s(cons(s(y0), y1))), z1))) MARK(length(and(length(s(cons(and(cons(y0, y1), y2), y3))), z1))) -> c9(MARK(and(length(s(cons(and(cons(y0, y1), y2), y3))), z1))) MARK(length(and(length(s(cons(and(tt, y0), y1))), z1))) -> c9(MARK(and(length(s(cons(and(tt, y0), y1))), z1))) MARK(length(and(length(s(cons(and(s(y0), y1), 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y2), y3)))) MARK(length(length(and(and(s(cons(length(length(cons(y0, y1))), y2)), y3), y4)))) -> c9(MARK(length(and(and(s(cons(length(length(cons(y0, y1))), y2)), y3), y4)))) MARK(length(length(and(and(s(cons(length(length(s(y0))), y1)), y2), y3)))) -> c9(MARK(length(and(and(s(cons(length(length(s(y0))), y1)), y2), y3)))) MARK(length(length(and(and(s(cons(length(length(y0)), y1)), y2), y3)))) -> c9(MARK(length(and(and(s(cons(length(length(y0)), y1)), y2), y3)))) MARK(length(length(and(and(s(cons(length(zeros), y0)), y1), y2)))) -> c9(MARK(length(and(and(s(cons(length(zeros), y0)), y1), y2)))) MARK(length(length(and(length(and(and(y0, y1), y2)), y3)))) -> c9(MARK(length(and(length(and(and(y0, y1), y2)), y3)))) MARK(length(length(and(length(and(length(y0), y1)), y2)))) -> c9(MARK(length(and(length(and(length(y0), y1)), y2)))) MARK(length(length(and(length(and(cons(y0, y1), y2)), y3)))) -> c9(MARK(length(and(length(and(cons(y0, y1), y2)), y3)))) MARK(length(length(and(length(and(tt, y0)), y1)))) -> c9(MARK(length(and(length(and(tt, y0)), y1)))) MARK(length(length(and(length(and(s(y0), y1)), y2)))) -> c9(MARK(length(and(length(and(s(y0), y1)), y2)))) MARK(length(length(and(length(and(zeros, y0)), y1)))) -> c9(MARK(length(and(length(and(zeros, y0)), y1)))) MARK(length(length(and(length(length(zeros)), y0)))) -> c9(MARK(length(and(length(length(zeros)), y0)))) MARK(length(length(and(length(length(and(y0, y1))), y2)))) -> c9(MARK(length(and(length(length(and(y0, y1))), y2)))) MARK(length(length(and(length(length(length(y0))), y1)))) -> c9(MARK(length(and(length(length(length(y0))), y1)))) MARK(length(length(and(length(length(cons(y0, y1))), y2)))) -> c9(MARK(length(and(length(length(cons(y0, y1))), y2)))) MARK(length(length(and(length(length(s(y0))), y1)))) -> c9(MARK(length(and(length(length(s(y0))), y1)))) MARK(length(length(and(length(s(s(y0))), y1)))) -> c9(MARK(length(and(length(s(s(y0))), y1)))) MARK(length(length(and(length(s(and(cons(y0, y1), y2))), y3)))) -> c9(MARK(length(and(length(s(and(cons(y0, y1), y2))), y3)))) MARK(length(length(and(length(s(and(tt, y0))), y1)))) -> c9(MARK(length(and(length(s(and(tt, y0))), y1)))) MARK(length(length(and(length(s(and(s(y0), y1))), y2)))) -> c9(MARK(length(and(length(s(and(s(y0), y1))), y2)))) MARK(length(length(and(length(s(length(cons(y0, y1)))), y2)))) -> c9(MARK(length(and(length(s(length(cons(y0, y1)))), y2)))) MARK(length(length(and(length(s(length(s(y0)))), y1)))) -> c9(MARK(length(and(length(s(length(s(y0)))), y1)))) MARK(length(length(and(length(s(and(and(and(y0, y1), y2), y3))), y4)))) -> c9(MARK(length(and(length(s(and(and(and(y0, y1), y2), y3))), y4)))) MARK(length(length(and(length(s(and(and(length(y0), y1), y2))), y3)))) -> c9(MARK(length(and(length(s(and(and(length(y0), y1), y2))), y3)))) MARK(length(length(and(length(s(and(and(cons(y0, y1), y2), y3))), y4)))) -> c9(MARK(length(and(length(s(and(and(cons(y0, y1), y2), y3))), y4)))) MARK(length(length(and(length(s(and(and(tt, y0), y1))), y2)))) -> c9(MARK(length(and(length(s(and(and(tt, y0), y1))), y2)))) MARK(length(length(and(length(s(and(and(s(y0), y1), y2))), y3)))) -> c9(MARK(length(and(length(s(and(and(s(y0), y1), y2))), y3)))) MARK(length(length(and(length(s(and(and(y0, y1), y2))), y3)))) -> c9(MARK(length(and(length(s(and(and(y0, y1), y2))), y3)))) MARK(length(length(and(length(s(and(length(zeros), y0))), y1)))) -> c9(MARK(length(and(length(s(and(length(zeros), y0))), y1)))) MARK(length(length(and(length(s(and(length(and(y0, y1)), y2))), y3)))) -> c9(MARK(length(and(length(s(and(length(and(y0, y1)), y2))), y3)))) MARK(length(length(and(length(s(and(length(length(y0)), y1))), y2)))) -> c9(MARK(length(and(length(s(and(length(length(y0)), y1))), y2)))) MARK(length(length(and(length(s(and(length(cons(y0, y1)), y2))), y3)))) -> c9(MARK(length(and(length(s(and(length(cons(y0, y1)), y2))), y3)))) MARK(length(length(and(length(s(and(length(s(y0)), y1))), y2)))) -> c9(MARK(length(and(length(s(and(length(s(y0)), y1))), y2)))) MARK(length(length(and(length(s(and(length(y0), y1))), y2)))) -> c9(MARK(length(and(length(s(and(length(y0), y1))), y2)))) MARK(length(length(and(length(s(and(and(zeros, y0), y1))), y2)))) -> c9(MARK(length(and(length(s(and(and(zeros, y0), y1))), y2)))) MARK(length(length(and(length(s(length(and(and(y0, y1), y2)))), y3)))) -> c9(MARK(length(and(length(s(length(and(and(y0, y1), y2)))), y3)))) MARK(length(length(and(length(s(length(and(length(y0), y1)))), y2)))) -> c9(MARK(length(and(length(s(length(and(length(y0), y1)))), y2)))) MARK(length(length(and(length(s(length(and(cons(y0, y1), y2)))), y3)))) -> c9(MARK(length(and(length(s(length(and(cons(y0, y1), y2)))), y3)))) MARK(length(length(and(length(s(length(and(tt, y0)))), y1)))) -> c9(MARK(length(and(length(s(length(and(tt, y0)))), y1)))) MARK(length(length(and(length(s(length(and(s(y0), y1)))), y2)))) -> c9(MARK(length(and(length(s(length(and(s(y0), y1)))), y2)))) MARK(length(length(and(length(s(length(and(y0, y1)))), y2)))) -> c9(MARK(length(and(length(s(length(and(y0, y1)))), y2)))) MARK(length(length(and(length(s(length(and(zeros, y0)))), y1)))) -> c9(MARK(length(and(length(s(length(and(zeros, y0)))), y1)))) MARK(length(length(and(length(s(length(length(zeros)))), y0)))) -> c9(MARK(length(and(length(s(length(length(zeros)))), y0)))) MARK(length(length(and(length(s(length(length(and(y0, y1))))), y2)))) -> c9(MARK(length(and(length(s(length(length(and(y0, y1))))), y2)))) MARK(length(length(and(length(s(length(length(length(y0))))), y1)))) -> c9(MARK(length(and(length(s(length(length(length(y0))))), y1)))) MARK(length(length(and(length(s(length(length(cons(y0, y1))))), y2)))) -> c9(MARK(length(and(length(s(length(length(cons(y0, y1))))), y2)))) MARK(length(length(and(length(s(length(length(s(y0))))), y1)))) -> c9(MARK(length(and(length(s(length(length(s(y0))))), y1)))) MARK(length(length(and(length(s(length(length(y0)))), y1)))) -> c9(MARK(length(and(length(s(length(length(y0)))), y1)))) MARK(length(length(and(length(s(length(zeros))), y0)))) -> c9(MARK(length(and(length(s(length(zeros))), y0)))) MARK(length(length(and(length(s(cons(cons(y0, y1), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(cons(y0, y1), y2))), y3)))) MARK(length(length(and(length(s(cons(s(y0), y1))), y2)))) -> c9(MARK(length(and(length(s(cons(s(y0), y1))), y2)))) MARK(length(length(and(length(s(cons(and(cons(y0, y1), y2), y3))), y4)))) -> c9(MARK(length(and(length(s(cons(and(cons(y0, y1), y2), y3))), y4)))) MARK(length(length(and(length(s(cons(and(tt, y0), y1))), y2)))) -> c9(MARK(length(and(length(s(cons(and(tt, y0), y1))), y2)))) MARK(length(length(and(length(s(cons(and(s(y0), y1), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(and(s(y0), y1), y2))), y3)))) MARK(length(length(and(length(s(cons(length(cons(y0, y1)), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(length(cons(y0, y1)), y2))), y3)))) MARK(length(length(and(length(s(cons(length(s(y0)), y1))), y2)))) -> c9(MARK(length(and(length(s(cons(length(s(y0)), y1))), y2)))) MARK(length(length(and(length(s(cons(and(and(and(y0, y1), y2), y3), y4))), y5)))) -> c9(MARK(length(and(length(s(cons(and(and(and(y0, y1), y2), y3), y4))), y5)))) MARK(length(length(and(length(s(cons(and(and(length(y0), y1), y2), y3))), y4)))) -> c9(MARK(length(and(length(s(cons(and(and(length(y0), y1), y2), y3))), y4)))) MARK(length(length(and(length(s(cons(and(and(cons(y0, y1), y2), y3), y4))), y5)))) -> c9(MARK(length(and(length(s(cons(and(and(cons(y0, y1), y2), y3), y4))), y5)))) MARK(length(length(and(length(s(cons(and(and(tt, y0), y1), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(and(and(tt, y0), y1), y2))), y3)))) MARK(length(length(and(length(s(cons(and(and(s(y0), y1), y2), y3))), y4)))) -> c9(MARK(length(and(length(s(cons(and(and(s(y0), y1), y2), y3))), y4)))) MARK(length(length(and(length(s(cons(and(and(y0, y1), y2), y3))), y4)))) -> c9(MARK(length(and(length(s(cons(and(and(y0, y1), y2), y3))), y4)))) MARK(length(length(and(length(s(cons(and(length(zeros), y0), y1))), y2)))) -> c9(MARK(length(and(length(s(cons(and(length(zeros), y0), y1))), y2)))) MARK(length(length(and(length(s(cons(and(length(and(y0, y1)), y2), y3))), y4)))) -> c9(MARK(length(and(length(s(cons(and(length(and(y0, y1)), y2), y3))), y4)))) MARK(length(length(and(length(s(cons(and(length(length(y0)), y1), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(and(length(length(y0)), y1), y2))), y3)))) MARK(length(length(and(length(s(cons(and(length(cons(y0, y1)), y2), y3))), y4)))) -> c9(MARK(length(and(length(s(cons(and(length(cons(y0, y1)), y2), y3))), y4)))) MARK(length(length(and(length(s(cons(and(length(s(y0)), y1), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(and(length(s(y0)), y1), y2))), y3)))) MARK(length(length(and(length(s(cons(and(length(y0), y1), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(and(length(y0), y1), y2))), y3)))) MARK(length(length(and(length(s(cons(and(and(zeros, y0), y1), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(and(and(zeros, y0), y1), y2))), y3)))) MARK(length(length(and(length(s(cons(length(and(and(y0, y1), y2)), y3))), y4)))) -> c9(MARK(length(and(length(s(cons(length(and(and(y0, y1), y2)), y3))), y4)))) MARK(length(length(and(length(s(cons(length(and(length(y0), y1)), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(length(and(length(y0), y1)), y2))), y3)))) MARK(length(length(and(length(s(cons(length(and(cons(y0, y1), y2)), y3))), y4)))) -> c9(MARK(length(and(length(s(cons(length(and(cons(y0, y1), y2)), y3))), y4)))) MARK(length(length(and(length(s(cons(length(and(tt, y0)), y1))), y2)))) -> c9(MARK(length(and(length(s(cons(length(and(tt, y0)), y1))), y2)))) MARK(length(length(and(length(s(cons(length(and(s(y0), y1)), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(length(and(s(y0), y1)), y2))), y3)))) MARK(length(length(and(length(s(cons(length(and(y0, y1)), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(length(and(y0, y1)), y2))), y3)))) MARK(length(length(and(length(s(cons(length(and(zeros, y0)), y1))), y2)))) -> c9(MARK(length(and(length(s(cons(length(and(zeros, y0)), y1))), y2)))) MARK(length(length(and(length(s(cons(length(length(zeros)), y0))), y1)))) -> c9(MARK(length(and(length(s(cons(length(length(zeros)), y0))), y1)))) MARK(length(length(and(length(s(cons(length(length(and(y0, y1))), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(length(length(and(y0, y1))), y2))), y3)))) MARK(length(length(and(length(s(cons(length(length(length(y0))), y1))), y2)))) -> c9(MARK(length(and(length(s(cons(length(length(length(y0))), y1))), y2)))) MARK(length(length(and(length(s(cons(length(length(cons(y0, y1))), y2))), y3)))) -> c9(MARK(length(and(length(s(cons(length(length(cons(y0, y1))), y2))), y3)))) MARK(length(length(and(length(s(cons(length(length(s(y0))), y1))), y2)))) -> c9(MARK(length(and(length(s(cons(length(length(s(y0))), y1))), y2)))) MARK(length(length(and(length(s(cons(length(length(y0)), y1))), y2)))) -> c9(MARK(length(and(length(s(cons(length(length(y0)), y1))), y2)))) MARK(length(length(and(length(s(cons(length(zeros), y0))), y1)))) -> c9(MARK(length(and(length(s(cons(length(zeros), y0))), y1)))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, mark_1 Defined Pair Symbols: A__LENGTH_1, MARK_1, A__AND_2 Compound Symbols: c5_2, c9_2, c5_1, c8_2, c8_1, c9_1, c2_1, c10_1, c14_1 ---------------------------------------- (193) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (194) 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__zeros -> cons(0, zeros) [1] a__and(tt, X) -> mark(X) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> s(a__length(mark(L))) [1] mark(zeros) -> a__zeros [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(tt) -> tt [1] mark(nil) -> nil [1] mark(s(X)) -> s(mark(X)) [1] a__zeros -> zeros [1] a__and(X1, X2) -> and(X1, X2) [1] a__length(X) -> length(X) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (195) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (196) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__zeros -> cons(0, zeros) [1] a__and(tt, X) -> mark(X) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> s(a__length(mark(L))) [1] mark(zeros) -> a__zeros [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(tt) -> tt [1] mark(nil) -> nil [1] mark(s(X)) -> s(mark(X)) [1] a__zeros -> zeros [1] a__and(X1, X2) -> and(X1, X2) [1] a__length(X) -> length(X) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:nil:s:and:length cons :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length 0 :: 0:zeros:cons:tt:nil:s:and:length zeros :: 0:zeros:cons:tt:nil:s:and:length a__and :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length tt :: 0:zeros:cons:tt:nil:s:and:length mark :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length a__length :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length nil :: 0:zeros:cons:tt:nil:s:and:length s :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length and :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length length :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length Rewrite Strategy: INNERMOST ---------------------------------------- (197) 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 ---------------------------------------- (198) 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__zeros -> cons(0, zeros) [1] a__and(tt, X) -> mark(X) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> s(a__length(mark(L))) [1] mark(zeros) -> a__zeros [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(tt) -> tt [1] mark(nil) -> nil [1] mark(s(X)) -> s(mark(X)) [1] a__zeros -> zeros [1] a__and(X1, X2) -> and(X1, X2) [1] a__length(X) -> length(X) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:nil:s:and:length cons :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length 0 :: 0:zeros:cons:tt:nil:s:and:length zeros :: 0:zeros:cons:tt:nil:s:and:length a__and :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length tt :: 0:zeros:cons:tt:nil:s:and:length mark :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length a__length :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length nil :: 0:zeros:cons:tt:nil:s:and:length s :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length and :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length length :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length Rewrite Strategy: INNERMOST ---------------------------------------- (199) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 zeros => 3 tt => 2 nil => 1 ---------------------------------------- (200) Obligation: Complexity RNTS consisting of the following rules: a__and(z, z') -{ 1 }-> mark(X) :|: z = 2, z' = X, X >= 0 a__and(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__length(z) -{ 1 }-> 0 :|: z = 1 a__length(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__length(z) -{ 1 }-> 1 + a__length(mark(L)) :|: z = 1 + N + L, L >= 0, N >= 0 a__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: mark(z) -{ 1 }-> a__zeros :|: z = 3 mark(z) -{ 1 }-> a__length(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__and(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> 2 :|: z = 2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (201) 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__zeros a__and_2 a__length_1 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (202) 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__zeros -> cons(0, zeros) [1] a__and(tt, X) -> mark(X) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> s(a__length(mark(L))) [1] mark(zeros) -> a__zeros [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(tt) -> tt [1] mark(nil) -> nil [1] mark(s(X)) -> s(mark(X)) [1] a__zeros -> zeros [1] a__and(X1, X2) -> and(X1, X2) [1] a__length(X) -> length(X) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:nil:s:and:length cons :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length 0 :: 0:zeros:cons:tt:nil:s:and:length zeros :: 0:zeros:cons:tt:nil:s:and:length a__and :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length tt :: 0:zeros:cons:tt:nil:s:and:length mark :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length a__length :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length nil :: 0:zeros:cons:tt:nil:s:and:length s :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length and :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length length :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length Rewrite Strategy: INNERMOST ---------------------------------------- (203) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (204) 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__zeros -> cons(0, zeros) [1] a__and(tt, X) -> mark(X) [1] a__length(nil) -> 0 [1] a__length(cons(N, zeros)) -> s(a__length(a__zeros)) [2] a__length(cons(N, and(X1', X2'))) -> s(a__length(a__and(mark(X1'), X2'))) [2] a__length(cons(N, length(X'))) -> s(a__length(a__length(mark(X')))) [2] a__length(cons(N, cons(X1'', X2''))) -> s(a__length(cons(mark(X1''), X2''))) [2] a__length(cons(N, 0)) -> s(a__length(0)) [2] a__length(cons(N, tt)) -> s(a__length(tt)) [2] a__length(cons(N, nil)) -> s(a__length(nil)) [2] a__length(cons(N, s(X''))) -> s(a__length(s(mark(X'')))) [2] mark(zeros) -> a__zeros [1] mark(and(zeros, X2)) -> a__and(a__zeros, X2) [2] mark(and(and(X11, X21), X2)) -> a__and(a__and(mark(X11), X21), X2) [2] mark(and(length(X3), X2)) -> a__and(a__length(mark(X3)), X2) [2] mark(and(cons(X12, X22), X2)) -> a__and(cons(mark(X12), X22), X2) [2] mark(and(0, X2)) -> a__and(0, X2) [2] mark(and(tt, X2)) -> a__and(tt, X2) [2] mark(and(nil, X2)) -> a__and(nil, X2) [2] mark(and(s(X4), X2)) -> a__and(s(mark(X4)), X2) [2] mark(length(zeros)) -> a__length(a__zeros) [2] mark(length(and(X13, X23))) -> a__length(a__and(mark(X13), X23)) [2] mark(length(length(X5))) -> a__length(a__length(mark(X5))) [2] mark(length(cons(X14, X24))) -> a__length(cons(mark(X14), X24)) [2] mark(length(0)) -> a__length(0) [2] mark(length(tt)) -> a__length(tt) [2] mark(length(nil)) -> a__length(nil) [2] mark(length(s(X6))) -> a__length(s(mark(X6))) [2] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(tt) -> tt [1] mark(nil) -> nil [1] mark(s(X)) -> s(mark(X)) [1] a__zeros -> zeros [1] a__and(X1, X2) -> and(X1, X2) [1] a__length(X) -> length(X) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:nil:s:and:length cons :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length 0 :: 0:zeros:cons:tt:nil:s:and:length zeros :: 0:zeros:cons:tt:nil:s:and:length a__and :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length tt :: 0:zeros:cons:tt:nil:s:and:length mark :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length a__length :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length nil :: 0:zeros:cons:tt:nil:s:and:length s :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length and :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length length :: 0:zeros:cons:tt:nil:s:and:length -> 0:zeros:cons:tt:nil:s:and:length Rewrite Strategy: INNERMOST ---------------------------------------- (205) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 zeros => 3 tt => 2 nil => 1 ---------------------------------------- (206) Obligation: Complexity RNTS consisting of the following rules: a__and(z, z') -{ 1 }-> mark(X) :|: z = 2, z' = X, X >= 0 a__and(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__length(z) -{ 1 }-> 0 :|: z = 1 a__length(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__length(z) -{ 2 }-> 1 + a__length(a__zeros) :|: z = 1 + N + 3, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(a__length(mark(X'))) :|: z = 1 + N + (1 + X'), X' >= 0, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(a__and(mark(X1'), X2')) :|: X2' >= 0, z = 1 + N + (1 + X1' + X2'), X1' >= 0, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(2) :|: z = 1 + N + 2, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(1) :|: z = 1 + N + 1, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(0) :|: z = 1 + N + 0, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(1 + mark(X'')) :|: z = 1 + N + (1 + X''), X'' >= 0, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(1 + mark(X1'') + X2'') :|: X1'' >= 0, X2'' >= 0, z = 1 + N + (1 + X1'' + X2''), N >= 0 a__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: mark(z) -{ 1 }-> a__zeros :|: z = 3 mark(z) -{ 2 }-> a__length(a__zeros) :|: z = 1 + 3 mark(z) -{ 2 }-> a__length(a__length(mark(X5))) :|: X5 >= 0, z = 1 + (1 + X5) mark(z) -{ 2 }-> a__length(a__and(mark(X13), X23)) :|: z = 1 + (1 + X13 + X23), X13 >= 0, X23 >= 0 mark(z) -{ 2 }-> a__length(2) :|: z = 1 + 2 mark(z) -{ 2 }-> a__length(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__length(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__length(1 + mark(X6)) :|: X6 >= 0, z = 1 + (1 + X6) mark(z) -{ 2 }-> a__length(1 + mark(X14) + X24) :|: z = 1 + (1 + X14 + X24), X14 >= 0, X24 >= 0 mark(z) -{ 2 }-> a__and(a__zeros, X2) :|: X2 >= 0, z = 1 + 3 + X2 mark(z) -{ 2 }-> a__and(a__length(mark(X3)), X2) :|: z = 1 + (1 + X3) + X2, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__and(mark(X11), X21), X2) :|: z = 1 + (1 + X11 + X21) + X2, X11 >= 0, X21 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(2, X2) :|: z = 1 + 2 + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(1 + mark(X4), X2) :|: X4 >= 0, X2 >= 0, z = 1 + (1 + X4) + X2 mark(z) -{ 2 }-> a__and(1 + mark(X12) + X22, X2) :|: z = 1 + (1 + X12 + X22) + X2, X12 >= 0, X22 >= 0, X2 >= 0 mark(z) -{ 1 }-> 2 :|: z = 2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 ---------------------------------------- (207) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: a__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: ---------------------------------------- (208) Obligation: Complexity RNTS consisting of the following rules: a__and(z, z') -{ 1 }-> mark(X) :|: z = 2, z' = X, X >= 0 a__and(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__length(z) -{ 1 }-> 0 :|: z = 1 a__length(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__length(z) -{ 2 }-> 1 + a__length(a__length(mark(X'))) :|: z = 1 + N + (1 + X'), X' >= 0, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(a__and(mark(X1'), X2')) :|: X2' >= 0, z = 1 + N + (1 + X1' + X2'), X1' >= 0, N >= 0 a__length(z) -{ 3 }-> 1 + a__length(3) :|: z = 1 + N + 3, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(2) :|: z = 1 + N + 2, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(1) :|: z = 1 + N + 1, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(0) :|: z = 1 + N + 0, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(1 + mark(X'')) :|: z = 1 + N + (1 + X''), X'' >= 0, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(1 + mark(X1'') + X2'') :|: X1'' >= 0, X2'' >= 0, z = 1 + N + (1 + X1'' + X2''), N >= 0 a__length(z) -{ 3 }-> 1 + a__length(1 + 0 + 3) :|: z = 1 + N + 3, N >= 0 a__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: mark(z) -{ 2 }-> a__length(a__length(mark(X5))) :|: X5 >= 0, z = 1 + (1 + X5) mark(z) -{ 2 }-> a__length(a__and(mark(X13), X23)) :|: z = 1 + (1 + X13 + X23), X13 >= 0, X23 >= 0 mark(z) -{ 3 }-> a__length(3) :|: z = 1 + 3 mark(z) -{ 2 }-> a__length(2) :|: z = 1 + 2 mark(z) -{ 2 }-> a__length(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__length(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__length(1 + mark(X6)) :|: X6 >= 0, z = 1 + (1 + X6) mark(z) -{ 2 }-> a__length(1 + mark(X14) + X24) :|: z = 1 + (1 + X14 + X24), X14 >= 0, X24 >= 0 mark(z) -{ 3 }-> a__length(1 + 0 + 3) :|: z = 1 + 3 mark(z) -{ 2 }-> a__and(a__length(mark(X3)), X2) :|: z = 1 + (1 + X3) + X2, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__and(mark(X11), X21), X2) :|: z = 1 + (1 + X11 + X21) + X2, X11 >= 0, X21 >= 0, X2 >= 0 mark(z) -{ 3 }-> a__and(3, X2) :|: X2 >= 0, z = 1 + 3 + X2 mark(z) -{ 2 }-> a__and(2, X2) :|: z = 1 + 2 + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(1 + mark(X4), X2) :|: X4 >= 0, X2 >= 0, z = 1 + (1 + X4) + X2 mark(z) -{ 2 }-> a__and(1 + mark(X12) + X22, X2) :|: z = 1 + (1 + X12 + X22) + X2, X12 >= 0, X22 >= 0, X2 >= 0 mark(z) -{ 3 }-> a__and(1 + 0 + 3, X2) :|: X2 >= 0, z = 1 + 3 + X2 mark(z) -{ 2 }-> 3 :|: z = 3 mark(z) -{ 1 }-> 2 :|: z = 2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> 1 + 0 + 3 :|: z = 3 ---------------------------------------- (209) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (210) Obligation: Complexity RNTS consisting of the following rules: a__and(z, z') -{ 1 }-> mark(z') :|: z = 2, z' >= 0 a__and(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__length(z) -{ 1 }-> 0 :|: z = 1 a__length(z) -{ 1 }-> 1 + z :|: z >= 0 a__length(z) -{ 2 }-> 1 + a__length(a__length(mark(X'))) :|: z = 1 + N + (1 + X'), X' >= 0, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(a__and(mark(X1'), X2')) :|: X2' >= 0, z = 1 + N + (1 + X1' + X2'), X1' >= 0, N >= 0 a__length(z) -{ 3 }-> 1 + a__length(3) :|: z - 4 >= 0 a__length(z) -{ 2 }-> 1 + a__length(2) :|: z - 3 >= 0 a__length(z) -{ 2 }-> 1 + a__length(1) :|: z - 2 >= 0 a__length(z) -{ 2 }-> 1 + a__length(0) :|: z - 1 >= 0 a__length(z) -{ 2 }-> 1 + a__length(1 + mark(X'')) :|: z = 1 + N + (1 + X''), X'' >= 0, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(1 + mark(X1'') + X2'') :|: X1'' >= 0, X2'' >= 0, z = 1 + N + (1 + X1'' + X2''), N >= 0 a__length(z) -{ 3 }-> 1 + a__length(1 + 0 + 3) :|: z - 4 >= 0 a__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: mark(z) -{ 2 }-> a__length(a__length(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__length(a__and(mark(X13), X23)) :|: z = 1 + (1 + X13 + X23), X13 >= 0, X23 >= 0 mark(z) -{ 3 }-> a__length(3) :|: z = 1 + 3 mark(z) -{ 2 }-> a__length(2) :|: z = 1 + 2 mark(z) -{ 2 }-> a__length(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__length(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__length(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__length(1 + mark(X14) + X24) :|: z = 1 + (1 + X14 + X24), X14 >= 0, X24 >= 0 mark(z) -{ 3 }-> a__length(1 + 0 + 3) :|: z = 1 + 3 mark(z) -{ 2 }-> a__and(a__length(mark(X3)), X2) :|: z = 1 + (1 + X3) + X2, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__and(mark(X11), X21), X2) :|: z = 1 + (1 + X11 + X21) + X2, X11 >= 0, X21 >= 0, X2 >= 0 mark(z) -{ 3 }-> a__and(3, z - 4) :|: z - 4 >= 0 mark(z) -{ 2 }-> a__and(2, z - 3) :|: z - 3 >= 0 mark(z) -{ 2 }-> a__and(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__and(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__and(1 + mark(X4), X2) :|: X4 >= 0, X2 >= 0, z = 1 + (1 + X4) + X2 mark(z) -{ 2 }-> a__and(1 + mark(X12) + X22, X2) :|: z = 1 + (1 + X12 + X22) + X2, X12 >= 0, X22 >= 0, X2 >= 0 mark(z) -{ 3 }-> a__and(1 + 0 + 3, z - 4) :|: z - 4 >= 0 mark(z) -{ 2 }-> 3 :|: z = 3 mark(z) -{ 1 }-> 2 :|: z = 2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(z - 1) :|: z - 1 >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> 1 + 0 + 3 :|: z = 3