KILLED proof of input_pzG5IgX0hw.trs # AProVE Commit ID: 5b976082cb74a395683ed8cc7acf94bd611ab29f fuhs 20230524 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).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), 38 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 1638 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 2701 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), 73 ms] (38) CpxTypedWeightedCompleteTrs (39) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (40) CpxRNTS (41) InliningProof [UPPER BOUND(ID), 523 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), 0 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), 13 ms] (68) CdtProblem (69) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtRhsSimplificationProcessorProof [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) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8 ms] (92) CdtProblem (93) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 14 ms] (96) CdtProblem (97) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22 ms] (130) CdtProblem (131) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 15 ms] (136) CdtProblem (137) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 43 ms] (142) CdtProblem (143) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 68 ms] (148) CdtProblem (149) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2 ms] (154) CdtProblem (155) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 5 ms] (156) CdtProblem (157) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 35 ms] (160) CdtProblem (161) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms] (164) CdtProblem (165) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 124 ms] (168) CdtProblem (169) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (170) CdtProblem (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 39 ms] (172) CdtProblem (173) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (174) CdtProblem (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (176) CdtProblem (177) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (178) CdtProblem (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 76 ms] (180) CdtProblem (181) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (182) CdtProblem (183) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 53 ms] (184) CdtProblem (185) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 26 ms] (186) CdtProblem (187) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 134 ms] (188) CdtProblem (189) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (190) CdtProblem (191) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 92 ms] (192) CdtProblem (193) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (194) CdtProblem (195) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 97 ms] (196) CdtProblem (197) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (198) CdtProblem (199) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 19 ms] (200) CdtProblem (201) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 145 ms] (202) CdtProblem (203) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (204) CdtProblem (205) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (206) CdtProblem (207) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 162 ms] (208) CdtProblem (209) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (210) CdtProblem (211) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (212) CdtProblem (213) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 208 ms] (214) CdtProblem (215) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 25 ms] (216) CdtProblem (217) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 30 ms] (218) CdtProblem (219) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 245 ms] (220) CdtProblem (221) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 52 ms] (222) CdtProblem (223) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 22 ms] (224) CdtProblem (225) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 95 ms] (226) CdtProblem (227) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (228) CdtProblem (229) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 727 ms] (230) CdtProblem (231) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (232) CdtProblem (233) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 717 ms] (234) CdtProblem (235) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (236) CdtProblem (237) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1235 ms] (238) CdtProblem (239) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 22 ms] (240) CdtProblem (241) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1284 ms] (242) CdtProblem (243) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (244) CdtProblem (245) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1196 ms] (246) CdtProblem (247) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 6 ms] (248) CdtProblem (249) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4333 ms] (250) CdtProblem (251) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (252) CdtProblem (253) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (254) CpxWeightedTrs (255) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (256) CpxTypedWeightedTrs (257) CompletionProof [UPPER BOUND(ID), 0 ms] (258) CpxTypedWeightedCompleteTrs (259) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (260) CpxTypedWeightedCompleteTrs (261) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 4 ms] (262) CpxRNTS (263) InliningProof [UPPER BOUND(ID), 247 ms] (264) CpxRNTS (265) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (266) CpxRNTS (267) CompletionProof [UPPER BOUND(ID), 0 ms] (268) CpxTypedWeightedCompleteTrs (269) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 2 ms] (270) 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))) a__take(0, IL) -> nil a__take(s(M), cons(N, IL)) -> cons(mark(N), take(M, IL)) mark(zeros) -> a__zeros mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(length(X)) -> a__length(mark(X)) mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) 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) a__take(X1, X2) -> take(X1, X2) 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))) a__take(0', IL) -> nil a__take(s(M), cons(N, IL)) -> cons(mark(N), take(M, IL)) mark(zeros) -> a__zeros mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(length(X)) -> a__length(mark(X)) mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) 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) a__take(X1, X2) -> take(X1, X2) 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))) a__take(0, IL) -> nil a__take(s(M), cons(N, IL)) -> cons(mark(N), take(M, IL)) mark(zeros) -> a__zeros mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(length(X)) -> a__length(mark(X)) mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) 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) a__take(X1, X2) -> take(X1, X2) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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 A__TAKE(0, z0) -> c7 A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) A__TAKE(z0, z1) -> c9 MARK(zeros) -> c10(A__ZEROS) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(0) -> c16 MARK(tt) -> c17 MARK(nil) -> c18 MARK(s(z0)) -> c19(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 A__TAKE(0, z0) -> c7 A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) A__TAKE(z0, z1) -> c9 MARK(zeros) -> c10(A__ZEROS) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(0) -> c16 MARK(tt) -> c17 MARK(nil) -> c18 MARK(s(z0)) -> c19(MARK(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__ZEROS, A__AND_2, A__LENGTH_1, A__TAKE_2, MARK_1 Compound Symbols: c, c1, c2_1, c3, c4, c5_2, c6, c7, c8_1, c9, c10_1, c11_2, c12_2, c13_2, c14_2, c15_1, c16, c17, c18, c19_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 A__TAKE(0, z0) -> c7 A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) A__TAKE(z0, z1) -> c9 MARK(zeros) -> c10(A__ZEROS) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(0) -> c16 MARK(tt) -> c17 MARK(nil) -> c18 MARK(s(z0)) -> c19(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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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 A__TAKE(0', z0) -> c7 A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) A__TAKE(z0, z1) -> c9 MARK(zeros) -> c10(A__ZEROS) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(0') -> c16 MARK(tt) -> c17 MARK(nil) -> c18 MARK(s(z0)) -> c19(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) a__take(0', z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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 A__TAKE(0', z0) -> c7 A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) A__TAKE(z0, z1) -> c9 MARK(zeros) -> c10(A__ZEROS) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(0') -> c16 MARK(tt) -> c17 MARK(nil) -> c18 MARK(s(z0)) -> c19(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) a__take(0', z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> c2:c3 tt :: tt:nil:cons:0':s:zeros:and:length:take c2 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c2:c3 MARK :: tt:nil:cons:0':s:zeros:and:length:take -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c3 :: c2:c3 A__LENGTH :: tt:nil:cons:0':s:zeros:and:length:take -> c4:c5:c6 nil :: tt:nil:cons:0':s:zeros:and:length:take c4 :: c4:c5:c6 cons :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c5 :: c4:c5:c6 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c4:c5:c6 mark :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c6 :: c4:c5:c6 A__TAKE :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> c7:c8:c9 0' :: tt:nil:cons:0':s:zeros:and:length:take c7 :: c7:c8:c9 s :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c8 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c7:c8:c9 c9 :: c7:c8:c9 zeros :: tt:nil:cons:0':s:zeros:and:length:take c10 :: c:c1 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 and :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c11 :: c2:c3 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 length :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c12 :: c4:c5:c6 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 take :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c13 :: c7:c8:c9 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c14 :: c7:c8:c9 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c15 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c16 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c17 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c18 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c19 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 a__zeros :: tt:nil:cons:0':s:zeros:and:length:take a__and :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take a__length :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take a__take :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take hole_c:c11_20 :: c:c1 hole_c2:c32_20 :: c2:c3 hole_tt:nil:cons:0':s:zeros:and:length:take3_20 :: tt:nil:cons:0':s:zeros:and:length:take hole_c10:c11:c12:c13:c14:c15:c16:c17:c18:c194_20 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 hole_c4:c5:c65_20 :: c4:c5:c6 hole_c7:c8:c96_20 :: c7:c8:c9 gen_tt:nil:cons:0':s:zeros:and:length:take7_20 :: Nat -> tt:nil:cons:0':s:zeros:and:length:take gen_c10:c11:c12:c13:c14:c15:c16:c17:c18:c198_20 :: Nat -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 gen_c4:c5:c69_20 :: 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 A__TAKE(0', z0) -> c7 A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) A__TAKE(z0, z1) -> c9 MARK(zeros) -> c10(A__ZEROS) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(0') -> c16 MARK(tt) -> c17 MARK(nil) -> c18 MARK(s(z0)) -> c19(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) a__take(0', z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> c2:c3 tt :: tt:nil:cons:0':s:zeros:and:length:take c2 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c2:c3 MARK :: tt:nil:cons:0':s:zeros:and:length:take -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c3 :: c2:c3 A__LENGTH :: tt:nil:cons:0':s:zeros:and:length:take -> c4:c5:c6 nil :: tt:nil:cons:0':s:zeros:and:length:take c4 :: c4:c5:c6 cons :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c5 :: c4:c5:c6 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c4:c5:c6 mark :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c6 :: c4:c5:c6 A__TAKE :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> c7:c8:c9 0' :: tt:nil:cons:0':s:zeros:and:length:take c7 :: c7:c8:c9 s :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c8 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c7:c8:c9 c9 :: c7:c8:c9 zeros :: tt:nil:cons:0':s:zeros:and:length:take c10 :: c:c1 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 and :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c11 :: c2:c3 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 length :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c12 :: c4:c5:c6 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 take :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c13 :: c7:c8:c9 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c14 :: c7:c8:c9 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c15 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c16 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c17 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c18 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c19 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 a__zeros :: tt:nil:cons:0':s:zeros:and:length:take a__and :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take a__length :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take a__take :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take hole_c:c11_20 :: c:c1 hole_c2:c32_20 :: c2:c3 hole_tt:nil:cons:0':s:zeros:and:length:take3_20 :: tt:nil:cons:0':s:zeros:and:length:take hole_c10:c11:c12:c13:c14:c15:c16:c17:c18:c194_20 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 hole_c4:c5:c65_20 :: c4:c5:c6 hole_c7:c8:c96_20 :: c7:c8:c9 gen_tt:nil:cons:0':s:zeros:and:length:take7_20 :: Nat -> tt:nil:cons:0':s:zeros:and:length:take gen_c10:c11:c12:c13:c14:c15:c16:c17:c18:c198_20 :: Nat -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 gen_c4:c5:c69_20 :: Nat -> c4:c5:c6 Generator Equations: gen_tt:nil:cons:0':s:zeros:and:length:take7_20(0) <=> tt gen_tt:nil:cons:0':s:zeros:and:length:take7_20(+(x, 1)) <=> cons(tt, gen_tt:nil:cons:0':s:zeros:and:length:take7_20(x)) gen_c10:c11:c12:c13:c14:c15:c16:c17:c18:c198_20(0) <=> c10(c) gen_c10:c11:c12:c13:c14:c15:c16:c17:c18:c198_20(+(x, 1)) <=> c11(c2(c10(c)), gen_c10:c11:c12:c13:c14:c15:c16:c17:c18:c198_20(x)) gen_c4:c5:c69_20(0) <=> c4 gen_c4:c5:c69_20(+(x, 1)) <=> c5(gen_c4:c5:c69_20(x), c10(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:0':s:zeros:and:length:take7_20(+(1, n11_20))) -> *10_20, rt in Omega(0) Induction Base: a__length(gen_tt:nil:cons:0':s:zeros:and:length:take7_20(+(1, 0))) Induction Step: a__length(gen_tt:nil:cons:0':s:zeros:and:length:take7_20(+(1, +(n11_20, 1)))) ->_R^Omega(0) s(a__length(mark(gen_tt:nil:cons:0':s:zeros:and:length:take7_20(+(1, n11_20))))) ->_R^Omega(0) s(a__length(cons(mark(tt), gen_tt:nil:cons:0':s:zeros:and:length:take7_20(n11_20)))) ->_R^Omega(0) s(a__length(cons(tt, gen_tt:nil:cons:0':s:zeros:and:length:take7_20(n11_20)))) ->_IH s(*10_20) 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 A__TAKE(0', z0) -> c7 A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) A__TAKE(z0, z1) -> c9 MARK(zeros) -> c10(A__ZEROS) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(0') -> c16 MARK(tt) -> c17 MARK(nil) -> c18 MARK(s(z0)) -> c19(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) a__take(0', z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> c2:c3 tt :: tt:nil:cons:0':s:zeros:and:length:take c2 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c2:c3 MARK :: tt:nil:cons:0':s:zeros:and:length:take -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c3 :: c2:c3 A__LENGTH :: tt:nil:cons:0':s:zeros:and:length:take -> c4:c5:c6 nil :: tt:nil:cons:0':s:zeros:and:length:take c4 :: c4:c5:c6 cons :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c5 :: c4:c5:c6 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c4:c5:c6 mark :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c6 :: c4:c5:c6 A__TAKE :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> c7:c8:c9 0' :: tt:nil:cons:0':s:zeros:and:length:take c7 :: c7:c8:c9 s :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c8 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c7:c8:c9 c9 :: c7:c8:c9 zeros :: tt:nil:cons:0':s:zeros:and:length:take c10 :: c:c1 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 and :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c11 :: c2:c3 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 length :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c12 :: c4:c5:c6 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 take :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c13 :: c7:c8:c9 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c14 :: c7:c8:c9 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c15 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c16 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c17 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c18 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c19 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 a__zeros :: tt:nil:cons:0':s:zeros:and:length:take a__and :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take a__length :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take a__take :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take hole_c:c11_20 :: c:c1 hole_c2:c32_20 :: c2:c3 hole_tt:nil:cons:0':s:zeros:and:length:take3_20 :: tt:nil:cons:0':s:zeros:and:length:take hole_c10:c11:c12:c13:c14:c15:c16:c17:c18:c194_20 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 hole_c4:c5:c65_20 :: c4:c5:c6 hole_c7:c8:c96_20 :: c7:c8:c9 gen_tt:nil:cons:0':s:zeros:and:length:take7_20 :: Nat -> tt:nil:cons:0':s:zeros:and:length:take gen_c10:c11:c12:c13:c14:c15:c16:c17:c18:c198_20 :: Nat -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 gen_c4:c5:c69_20 :: Nat -> c4:c5:c6 Lemmas: a__length(gen_tt:nil:cons:0':s:zeros:and:length:take7_20(+(1, n11_20))) -> *10_20, rt in Omega(0) Generator Equations: gen_tt:nil:cons:0':s:zeros:and:length:take7_20(0) <=> tt gen_tt:nil:cons:0':s:zeros:and:length:take7_20(+(x, 1)) <=> cons(tt, gen_tt:nil:cons:0':s:zeros:and:length:take7_20(x)) gen_c10:c11:c12:c13:c14:c15:c16:c17:c18:c198_20(0) <=> c10(c) gen_c10:c11:c12:c13:c14:c15:c16:c17:c18:c198_20(+(x, 1)) <=> c11(c2(c10(c)), gen_c10:c11:c12:c13:c14:c15:c16:c17:c18:c198_20(x)) gen_c4:c5:c69_20(0) <=> c4 gen_c4:c5:c69_20(+(x, 1)) <=> c5(gen_c4:c5:c69_20(x), c10(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:0':s:zeros:and:length:take7_20(+(1, n39957_20))) -> *10_20, rt in Omega(n39957_20) Induction Base: A__LENGTH(gen_tt:nil:cons:0':s:zeros:and:length:take7_20(+(1, 0))) Induction Step: A__LENGTH(gen_tt:nil:cons:0':s:zeros:and:length:take7_20(+(1, +(n39957_20, 1)))) ->_R^Omega(1) c5(A__LENGTH(mark(gen_tt:nil:cons:0':s:zeros:and:length:take7_20(+(1, n39957_20)))), MARK(gen_tt:nil:cons:0':s:zeros:and:length:take7_20(+(1, n39957_20)))) ->_R^Omega(0) c5(A__LENGTH(cons(mark(tt), gen_tt:nil:cons:0':s:zeros:and:length:take7_20(n39957_20))), MARK(gen_tt:nil:cons:0':s:zeros:and:length:take7_20(+(1, n39957_20)))) ->_R^Omega(0) c5(A__LENGTH(cons(tt, gen_tt:nil:cons:0':s:zeros:and:length:take7_20(n39957_20))), MARK(gen_tt:nil:cons:0':s:zeros:and:length:take7_20(+(1, n39957_20)))) ->_IH c5(*10_20, MARK(gen_tt:nil:cons:0':s:zeros:and:length:take7_20(+(1, n39957_20)))) ->_R^Omega(1) c5(*10_20, c15(MARK(tt))) ->_R^Omega(1) c5(*10_20, c15(c17)) 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 A__TAKE(0', z0) -> c7 A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) A__TAKE(z0, z1) -> c9 MARK(zeros) -> c10(A__ZEROS) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(0') -> c16 MARK(tt) -> c17 MARK(nil) -> c18 MARK(s(z0)) -> c19(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) a__take(0', z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> c2:c3 tt :: tt:nil:cons:0':s:zeros:and:length:take c2 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c2:c3 MARK :: tt:nil:cons:0':s:zeros:and:length:take -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c3 :: c2:c3 A__LENGTH :: tt:nil:cons:0':s:zeros:and:length:take -> c4:c5:c6 nil :: tt:nil:cons:0':s:zeros:and:length:take c4 :: c4:c5:c6 cons :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c5 :: c4:c5:c6 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c4:c5:c6 mark :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c6 :: c4:c5:c6 A__TAKE :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> c7:c8:c9 0' :: tt:nil:cons:0':s:zeros:and:length:take c7 :: c7:c8:c9 s :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c8 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c7:c8:c9 c9 :: c7:c8:c9 zeros :: tt:nil:cons:0':s:zeros:and:length:take c10 :: c:c1 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 and :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c11 :: c2:c3 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 length :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c12 :: c4:c5:c6 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 take :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c13 :: c7:c8:c9 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c14 :: c7:c8:c9 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c15 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c16 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c17 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c18 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c19 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 a__zeros :: tt:nil:cons:0':s:zeros:and:length:take a__and :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take a__length :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take a__take :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take hole_c:c11_20 :: c:c1 hole_c2:c32_20 :: c2:c3 hole_tt:nil:cons:0':s:zeros:and:length:take3_20 :: tt:nil:cons:0':s:zeros:and:length:take hole_c10:c11:c12:c13:c14:c15:c16:c17:c18:c194_20 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 hole_c4:c5:c65_20 :: c4:c5:c6 hole_c7:c8:c96_20 :: c7:c8:c9 gen_tt:nil:cons:0':s:zeros:and:length:take7_20 :: Nat -> tt:nil:cons:0':s:zeros:and:length:take gen_c10:c11:c12:c13:c14:c15:c16:c17:c18:c198_20 :: Nat -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 gen_c4:c5:c69_20 :: Nat -> c4:c5:c6 Lemmas: a__length(gen_tt:nil:cons:0':s:zeros:and:length:take7_20(+(1, n11_20))) -> *10_20, rt in Omega(0) Generator Equations: gen_tt:nil:cons:0':s:zeros:and:length:take7_20(0) <=> tt gen_tt:nil:cons:0':s:zeros:and:length:take7_20(+(x, 1)) <=> cons(tt, gen_tt:nil:cons:0':s:zeros:and:length:take7_20(x)) gen_c10:c11:c12:c13:c14:c15:c16:c17:c18:c198_20(0) <=> c10(c) gen_c10:c11:c12:c13:c14:c15:c16:c17:c18:c198_20(+(x, 1)) <=> c11(c2(c10(c)), gen_c10:c11:c12:c13:c14:c15:c16:c17:c18:c198_20(x)) gen_c4:c5:c69_20(0) <=> c4 gen_c4:c5:c69_20(+(x, 1)) <=> c5(gen_c4:c5:c69_20(x), c10(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 A__TAKE(0', z0) -> c7 A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) A__TAKE(z0, z1) -> c9 MARK(zeros) -> c10(A__ZEROS) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(0') -> c16 MARK(tt) -> c17 MARK(nil) -> c18 MARK(s(z0)) -> c19(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) a__take(0', z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> c2:c3 tt :: tt:nil:cons:0':s:zeros:and:length:take c2 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c2:c3 MARK :: tt:nil:cons:0':s:zeros:and:length:take -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c3 :: c2:c3 A__LENGTH :: tt:nil:cons:0':s:zeros:and:length:take -> c4:c5:c6 nil :: tt:nil:cons:0':s:zeros:and:length:take c4 :: c4:c5:c6 cons :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c5 :: c4:c5:c6 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c4:c5:c6 mark :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c6 :: c4:c5:c6 A__TAKE :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> c7:c8:c9 0' :: tt:nil:cons:0':s:zeros:and:length:take c7 :: c7:c8:c9 s :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c8 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c7:c8:c9 c9 :: c7:c8:c9 zeros :: tt:nil:cons:0':s:zeros:and:length:take c10 :: c:c1 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 and :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c11 :: c2:c3 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 length :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c12 :: c4:c5:c6 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 take :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take c13 :: c7:c8:c9 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c14 :: c7:c8:c9 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c15 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c16 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c17 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c18 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 c19 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 a__zeros :: tt:nil:cons:0':s:zeros:and:length:take a__and :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take a__length :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take a__take :: tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take -> tt:nil:cons:0':s:zeros:and:length:take hole_c:c11_20 :: c:c1 hole_c2:c32_20 :: c2:c3 hole_tt:nil:cons:0':s:zeros:and:length:take3_20 :: tt:nil:cons:0':s:zeros:and:length:take hole_c10:c11:c12:c13:c14:c15:c16:c17:c18:c194_20 :: c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 hole_c4:c5:c65_20 :: c4:c5:c6 hole_c7:c8:c96_20 :: c7:c8:c9 gen_tt:nil:cons:0':s:zeros:and:length:take7_20 :: Nat -> tt:nil:cons:0':s:zeros:and:length:take gen_c10:c11:c12:c13:c14:c15:c16:c17:c18:c198_20 :: Nat -> c10:c11:c12:c13:c14:c15:c16:c17:c18:c19 gen_c4:c5:c69_20 :: Nat -> c4:c5:c6 Lemmas: a__length(gen_tt:nil:cons:0':s:zeros:and:length:take7_20(+(1, n11_20))) -> *10_20, rt in Omega(0) A__LENGTH(gen_tt:nil:cons:0':s:zeros:and:length:take7_20(+(1, n39957_20))) -> *10_20, rt in Omega(n39957_20) Generator Equations: gen_tt:nil:cons:0':s:zeros:and:length:take7_20(0) <=> tt gen_tt:nil:cons:0':s:zeros:and:length:take7_20(+(x, 1)) <=> cons(tt, gen_tt:nil:cons:0':s:zeros:and:length:take7_20(x)) gen_c10:c11:c12:c13:c14:c15:c16:c17:c18:c198_20(0) <=> c10(c) gen_c10:c11:c12:c13:c14:c15:c16:c17:c18:c198_20(+(x, 1)) <=> c11(c2(c10(c)), gen_c10:c11:c12:c13:c14:c15:c16:c17:c18:c198_20(x)) gen_c4:c5:c69_20(0) <=> c4 gen_c4:c5:c69_20(+(x, 1)) <=> c5(gen_c4:c5:c69_20(x), c10(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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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 A__TAKE(0, z0) -> c7 A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) A__TAKE(z0, z1) -> c9 MARK(zeros) -> c10(A__ZEROS) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(0) -> c16 MARK(tt) -> c17 MARK(nil) -> c18 MARK(s(z0)) -> c19(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 A__TAKE(0, z0) -> c7 A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) A__TAKE(z0, z1) -> c9 MARK(zeros) -> c10(A__ZEROS) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(0) -> c16 MARK(tt) -> c17 MARK(nil) -> c18 MARK(s(z0)) -> c19(MARK(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__ZEROS, A__AND_2, A__LENGTH_1, A__TAKE_2, MARK_1 Compound Symbols: c, c1, c2_1, c3, c4, c5_2, c6, c7, c8_1, c9, c10_1, c11_2, c12_2, c13_2, c14_2, c15_1, c16, c17, c18, c19_1 ---------------------------------------- (25) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 11 trailing nodes: MARK(nil) -> c18 MARK(zeros) -> c10(A__ZEROS) A__LENGTH(nil) -> c4 A__ZEROS -> c1 A__LENGTH(z0) -> c6 A__TAKE(z0, z1) -> c9 MARK(tt) -> c17 A__TAKE(0, z0) -> c7 MARK(0) -> c16 A__AND(z0, z1) -> c3 A__ZEROS -> c ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__LENGTH_1, A__TAKE_2, MARK_1 Compound Symbols: c2_1, c5_2, c8_1, c11_2, c12_2, c13_2, c14_2, c15_1, c19_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)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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] A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) [1] MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) [1] MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c15(MARK(z0)) [1] MARK(s(z0)) -> c19(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] a__take(0, z0) -> nil [0] a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) [0] a__take(z0, z1) -> take(z0, z1) [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(take(z0, z1)) -> a__take(mark(z0), mark(z1)) [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] A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) [1] MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) [1] MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c15(MARK(z0)) [1] MARK(s(z0)) -> c19(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] a__take(0, z0) -> nil [0] a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) [0] a__take(z0, z1) -> take(z0, z1) [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(take(z0, z1)) -> a__take(mark(z0), mark(z1)) [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:s:and:length:take:0:zeros:nil -> tt:cons:s:and:length:take:0:zeros:nil -> c2 tt :: tt:cons:s:and:length:take:0:zeros:nil c2 :: c11:c12:c13:c14:c15:c19 -> c2 MARK :: tt:cons:s:and:length:take:0:zeros:nil -> c11:c12:c13:c14:c15:c19 A__LENGTH :: tt:cons:s:and:length:take:0:zeros:nil -> c5 cons :: tt:cons:s:and:length:take:0:zeros:nil -> tt:cons:s:and:length:take:0:zeros:nil -> tt:cons:s:and:length:take:0:zeros:nil c5 :: c5 -> c11:c12:c13:c14:c15:c19 -> c5 mark :: tt:cons:s:and:length:take:0:zeros:nil -> tt:cons:s:and:length:take:0:zeros:nil A__TAKE :: tt:cons:s:and:length:take:0:zeros:nil -> tt:cons:s:and:length:take:0:zeros:nil -> c8 s :: tt:cons:s:and:length:take:0:zeros:nil -> tt:cons:s:and:length:take:0:zeros:nil c8 :: c11:c12:c13:c14:c15:c19 -> c8 and :: tt:cons:s:and:length:take:0:zeros:nil -> tt:cons:s:and:length:take:0:zeros:nil -> tt:cons:s:and:length:take:0:zeros:nil c11 :: c2 -> c11:c12:c13:c14:c15:c19 -> c11:c12:c13:c14:c15:c19 length :: tt:cons:s:and:length:take:0:zeros:nil -> tt:cons:s:and:length:take:0:zeros:nil c12 :: c5 -> c11:c12:c13:c14:c15:c19 -> c11:c12:c13:c14:c15:c19 take :: tt:cons:s:and:length:take:0:zeros:nil -> tt:cons:s:and:length:take:0:zeros:nil -> tt:cons:s:and:length:take:0:zeros:nil c13 :: c8 -> c11:c12:c13:c14:c15:c19 -> c11:c12:c13:c14:c15:c19 c14 :: c8 -> c11:c12:c13:c14:c15:c19 -> c11:c12:c13:c14:c15:c19 c15 :: c11:c12:c13:c14:c15:c19 -> c11:c12:c13:c14:c15:c19 c19 :: c11:c12:c13:c14:c15:c19 -> c11:c12:c13:c14:c15:c19 a__zeros :: tt:cons:s:and:length:take:0:zeros:nil 0 :: tt:cons:s:and:length:take:0:zeros:nil zeros :: tt:cons:s:and:length:take:0:zeros:nil a__and :: tt:cons:s:and:length:take:0:zeros:nil -> tt:cons:s:and:length:take:0:zeros:nil -> tt:cons:s:and:length:take:0:zeros:nil a__length :: tt:cons:s:and:length:take:0:zeros:nil -> tt:cons:s:and:length:take:0:zeros:nil nil :: tt:cons:s:and:length:take:0:zeros:nil a__take :: tt:cons:s:and:length:take:0:zeros:nil -> tt:cons:s:and:length:take:0:zeros:nil -> tt:cons:s:and:length:take: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 A__TAKE_2 MARK_1 (c) The following functions are completely defined: a__zeros a__and_2 a__length_1 a__take_2 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] a__take(v0, v1) -> null_a__take [0] mark(v0) -> null_mark [0] And the following fresh constants: null_a__zeros, null_a__and, null_a__length, null_a__take, null_mark, const, const1, const2, const3 ---------------------------------------- (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] A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) [1] MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) [1] MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c15(MARK(z0)) [1] MARK(s(z0)) -> c19(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] a__take(0, z0) -> nil [0] a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) [0] a__take(z0, z1) -> take(z0, z1) [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(take(z0, z1)) -> a__take(mark(z0), mark(z1)) [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] a__take(v0, v1) -> null_a__take [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__AND :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> c2 tt :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark c2 :: c11:c12:c13:c14:c15:c19 -> c2 MARK :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> c11:c12:c13:c14:c15:c19 A__LENGTH :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> c5 cons :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark c5 :: c5 -> c11:c12:c13:c14:c15:c19 -> c5 mark :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark A__TAKE :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> c8 s :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark c8 :: c11:c12:c13:c14:c15:c19 -> c8 and :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark c11 :: c2 -> c11:c12:c13:c14:c15:c19 -> c11:c12:c13:c14:c15:c19 length :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark c12 :: c5 -> c11:c12:c13:c14:c15:c19 -> c11:c12:c13:c14:c15:c19 take :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark c13 :: c8 -> c11:c12:c13:c14:c15:c19 -> c11:c12:c13:c14:c15:c19 c14 :: c8 -> c11:c12:c13:c14:c15:c19 -> c11:c12:c13:c14:c15:c19 c15 :: c11:c12:c13:c14:c15:c19 -> c11:c12:c13:c14:c15:c19 c19 :: c11:c12:c13:c14:c15:c19 -> c11:c12:c13:c14:c15:c19 a__zeros :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark 0 :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark zeros :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark a__and :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark a__length :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark nil :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark a__take :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark null_a__zeros :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark null_a__and :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark null_a__length :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark null_a__take :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark null_mark :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark const :: c2 const1 :: c11:c12:c13:c14:c15:c19 const2 :: c5 const3 :: c8 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, take(z01, z1''))) -> c5(A__LENGTH(a__take(mark(z01), mark(z1''))), MARK(take(z01, z1''))) [1] A__LENGTH(cons(z0, cons(z02, z11))) -> c5(A__LENGTH(cons(mark(z02), z11)), MARK(cons(z02, z11))) [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(z03))) -> c5(A__LENGTH(s(mark(z03))), MARK(s(z03))) [1] A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(null_mark), MARK(z1)) [1] A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) [1] MARK(and(zeros, z1)) -> c11(A__AND(a__zeros, z1), MARK(zeros)) [1] MARK(and(and(z04, z12), z1)) -> c11(A__AND(a__and(mark(z04), z12), z1), MARK(and(z04, z12))) [1] MARK(and(length(z05), z1)) -> c11(A__AND(a__length(mark(z05)), z1), MARK(length(z05))) [1] MARK(and(take(z06, z13), z1)) -> c11(A__AND(a__take(mark(z06), mark(z13)), z1), MARK(take(z06, z13))) [1] MARK(and(cons(z07, z14), z1)) -> c11(A__AND(cons(mark(z07), z14), z1), MARK(cons(z07, z14))) [1] MARK(and(0, z1)) -> c11(A__AND(0, z1), MARK(0)) [1] MARK(and(tt, z1)) -> c11(A__AND(tt, z1), MARK(tt)) [1] MARK(and(nil, z1)) -> c11(A__AND(nil, z1), MARK(nil)) [1] MARK(and(s(z08), z1)) -> c11(A__AND(s(mark(z08)), z1), MARK(s(z08))) [1] MARK(and(z0, z1)) -> c11(A__AND(null_mark, z1), MARK(z0)) [1] MARK(length(zeros)) -> c12(A__LENGTH(a__zeros), MARK(zeros)) [1] MARK(length(and(z09, z15))) -> c12(A__LENGTH(a__and(mark(z09), z15)), MARK(and(z09, z15))) [1] MARK(length(length(z010))) -> c12(A__LENGTH(a__length(mark(z010))), MARK(length(z010))) [1] MARK(length(take(z011, z16))) -> c12(A__LENGTH(a__take(mark(z011), mark(z16))), MARK(take(z011, z16))) [1] MARK(length(cons(z012, z17))) -> c12(A__LENGTH(cons(mark(z012), z17)), MARK(cons(z012, z17))) [1] MARK(length(0)) -> c12(A__LENGTH(0), MARK(0)) [1] MARK(length(tt)) -> c12(A__LENGTH(tt), MARK(tt)) [1] MARK(length(nil)) -> c12(A__LENGTH(nil), MARK(nil)) [1] MARK(length(s(z013))) -> c12(A__LENGTH(s(mark(z013))), MARK(s(z013))) [1] MARK(length(z0)) -> c12(A__LENGTH(null_mark), MARK(z0)) [1] MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c15(MARK(z0)) [1] MARK(s(z0)) -> c19(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(z0124, z174))) -> s(a__length(a__and(mark(z0124), z174))) [0] a__length(cons(z0, length(z0125))) -> s(a__length(a__length(mark(z0125)))) [0] a__length(cons(z0, take(z0126, z175))) -> s(a__length(a__take(mark(z0126), mark(z175)))) [0] a__length(cons(z0, cons(z0127, z176))) -> s(a__length(cons(mark(z0127), z176))) [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(z0128))) -> s(a__length(s(mark(z0128)))) [0] a__length(cons(z0, z1)) -> s(a__length(null_mark)) [0] a__length(z0) -> length(z0) [0] a__take(0, z0) -> nil [0] a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) [0] a__take(z0, z1) -> take(z0, z1) [0] mark(zeros) -> a__zeros [0] mark(and(zeros, z1)) -> a__and(a__zeros, z1) [0] mark(and(and(z0129, z177), z1)) -> a__and(a__and(mark(z0129), z177), z1) [0] mark(and(length(z0130), z1)) -> a__and(a__length(mark(z0130)), z1) [0] mark(and(take(z0131, z178), z1)) -> a__and(a__take(mark(z0131), mark(z178)), z1) [0] mark(and(cons(z0132, z179), z1)) -> a__and(cons(mark(z0132), z179), 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(z0133), z1)) -> a__and(s(mark(z0133)), z1) [0] mark(and(z0, z1)) -> a__and(null_mark, z1) [0] mark(length(zeros)) -> a__length(a__zeros) [0] mark(length(and(z0134, z180))) -> a__length(a__and(mark(z0134), z180)) [0] mark(length(length(z0135))) -> a__length(a__length(mark(z0135))) [0] mark(length(take(z0136, z181))) -> a__length(a__take(mark(z0136), mark(z181))) [0] mark(length(cons(z0137, z182))) -> a__length(cons(mark(z0137), z182)) [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(z0138))) -> a__length(s(mark(z0138))) [0] mark(length(z0)) -> a__length(null_mark) [0] mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) [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] a__take(v0, v1) -> null_a__take [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__AND :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> c2 tt :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark c2 :: c11:c12:c13:c14:c15:c19 -> c2 MARK :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> c11:c12:c13:c14:c15:c19 A__LENGTH :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> c5 cons :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark c5 :: c5 -> c11:c12:c13:c14:c15:c19 -> c5 mark :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark A__TAKE :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> c8 s :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark c8 :: c11:c12:c13:c14:c15:c19 -> c8 and :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark c11 :: c2 -> c11:c12:c13:c14:c15:c19 -> c11:c12:c13:c14:c15:c19 length :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark c12 :: c5 -> c11:c12:c13:c14:c15:c19 -> c11:c12:c13:c14:c15:c19 take :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark c13 :: c8 -> c11:c12:c13:c14:c15:c19 -> c11:c12:c13:c14:c15:c19 c14 :: c8 -> c11:c12:c13:c14:c15:c19 -> c11:c12:c13:c14:c15:c19 c15 :: c11:c12:c13:c14:c15:c19 -> c11:c12:c13:c14:c15:c19 c19 :: c11:c12:c13:c14:c15:c19 -> c11:c12:c13:c14:c15:c19 a__zeros :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark 0 :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark zeros :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark a__and :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark a__length :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark nil :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark a__take :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark null_a__zeros :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark null_a__and :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark null_a__length :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark null_a__take :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark null_mark :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark const :: c2 const1 :: c11:c12:c13:c14:c15:c19 const2 :: c5 const3 :: c8 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_a__take => 0 null_mark => 0 const => 0 const1 => 0 const2 => 0 const3 => 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__take(mark(z01), mark(z1''))) + MARK(1 + z01 + z1'') :|: z = 1 + z0 + (1 + z01 + z1''), z01 >= 0, z0 >= 0, z1'' >= 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(z03)) + MARK(1 + z03) :|: z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(1 + mark(z02) + z11) + MARK(1 + z02 + z11) :|: z = 1 + z0 + (1 + z02 + z11), z11 >= 0, z02 >= 0, z0 >= 0 A__TAKE(z, z') -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 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__TAKE(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__LENGTH(a__zeros) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__LENGTH(a__take(mark(z011), mark(z16))) + MARK(1 + z011 + z16) :|: z011 >= 0, z = 1 + (1 + z011 + z16), z16 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(a__length(mark(z010))) + MARK(1 + z010) :|: z = 1 + (1 + z010), z010 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(a__and(mark(z09), z15)) + MARK(1 + z09 + z15) :|: z15 >= 0, z09 >= 0, z = 1 + (1 + z09 + z15) 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(z013)) + MARK(1 + z013) :|: z013 >= 0, z = 1 + (1 + z013) MARK(z) -{ 1 }-> 1 + A__LENGTH(1 + mark(z012) + z17) + MARK(1 + z012 + z17) :|: z = 1 + (1 + z012 + z17), z17 >= 0, z012 >= 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__take(mark(z06), mark(z13)), z1) + MARK(1 + z06 + z13) :|: z1 >= 0, z = 1 + (1 + z06 + z13) + z1, z06 >= 0, z13 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__length(mark(z05)), z1) + MARK(1 + z05) :|: z1 >= 0, z = 1 + (1 + z05) + z1, z05 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__and(mark(z04), z12), z1) + MARK(1 + z04 + z12) :|: z04 >= 0, z = 1 + (1 + z04 + z12) + z1, z1 >= 0, z12 >= 0 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(z08), z1) + MARK(1 + z08) :|: z08 >= 0, z1 >= 0, z = 1 + (1 + z08) + z1 MARK(z) -{ 1 }-> 1 + A__AND(1 + mark(z07) + z14, z1) + MARK(1 + z07 + z14) :|: z1 >= 0, z07 >= 0, z = 1 + (1 + z07 + z14) + z1, z14 >= 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__take(mark(z0126), mark(z175))) :|: z = 1 + z0 + (1 + z0126 + z175), z0 >= 0, z175 >= 0, z0126 >= 0 a__length(z) -{ 0 }-> 1 + a__length(a__length(mark(z0125))) :|: z = 1 + z0 + (1 + z0125), z0 >= 0, z0125 >= 0 a__length(z) -{ 0 }-> 1 + a__length(a__and(mark(z0124), z174)) :|: z = 1 + z0 + (1 + z0124 + z174), z0 >= 0, z0124 >= 0, z174 >= 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(z0128)) :|: z0 >= 0, z0128 >= 0, z = 1 + z0 + (1 + z0128) a__length(z) -{ 0 }-> 1 + a__length(1 + mark(z0127) + z176) :|: z = 1 + z0 + (1 + z0127 + z176), z0 >= 0, z0127 >= 0, z176 >= 0 a__take(z, z') -{ 0 }-> 1 :|: z0 >= 0, z = 0, z' = z0 a__take(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__take(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__take(z, z') -{ 0 }-> 1 + mark(z1) + (1 + z0 + z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 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__take(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__length(a__zeros) :|: z = 1 + 3 mark(z) -{ 0 }-> a__length(a__take(mark(z0136), mark(z181))) :|: z0136 >= 0, z181 >= 0, z = 1 + (1 + z0136 + z181) mark(z) -{ 0 }-> a__length(a__length(mark(z0135))) :|: z = 1 + (1 + z0135), z0135 >= 0 mark(z) -{ 0 }-> a__length(a__and(mark(z0134), z180)) :|: z = 1 + (1 + z0134 + z180), z0134 >= 0, z180 >= 0 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(z0138)) :|: z = 1 + (1 + z0138), z0138 >= 0 mark(z) -{ 0 }-> a__length(1 + mark(z0137) + z182) :|: z182 >= 0, z0137 >= 0, z = 1 + (1 + z0137 + z182) mark(z) -{ 0 }-> a__and(a__zeros, z1) :|: z1 >= 0, z = 1 + 3 + z1 mark(z) -{ 0 }-> a__and(a__take(mark(z0131), mark(z178)), z1) :|: z1 >= 0, z = 1 + (1 + z0131 + z178) + z1, z0131 >= 0, z178 >= 0 mark(z) -{ 0 }-> a__and(a__length(mark(z0130)), z1) :|: z = 1 + (1 + z0130) + z1, z1 >= 0, z0130 >= 0 mark(z) -{ 0 }-> a__and(a__and(mark(z0129), z177), z1) :|: z1 >= 0, z0129 >= 0, z = 1 + (1 + z0129 + z177) + z1, z177 >= 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(z0133), z1) :|: z1 >= 0, z0133 >= 0, z = 1 + (1 + z0133) + z1 mark(z) -{ 0 }-> a__and(1 + mark(z0132) + z179, z1) :|: z0132 >= 0, z1 >= 0, z179 >= 0, z = 1 + (1 + z0132 + z179) + 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 ---------------------------------------- (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__take(mark(z01), mark(z1''))) + MARK(1 + z01 + z1'') :|: z = 1 + z0 + (1 + z01 + z1''), z01 >= 0, z0 >= 0, z1'' >= 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 = 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(z03)) + MARK(1 + z03) :|: z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(1 + mark(z02) + z11) + MARK(1 + z02 + z11) :|: z = 1 + z0 + (1 + z02 + z11), z11 >= 0, z02 >= 0, z0 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(1 + 0 + 3) + MARK(3) :|: z = 1 + z0 + 3, z0 >= 0 A__TAKE(z, z') -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 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__TAKE(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__LENGTH(a__take(mark(z011), mark(z16))) + MARK(1 + z011 + z16) :|: z011 >= 0, z = 1 + (1 + z011 + z16), z16 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(a__length(mark(z010))) + MARK(1 + z010) :|: z = 1 + (1 + z010), z010 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(a__and(mark(z09), z15)) + MARK(1 + z09 + z15) :|: z15 >= 0, z09 >= 0, z = 1 + (1 + z09 + z15) 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(z013)) + MARK(1 + z013) :|: z013 >= 0, z = 1 + (1 + z013) MARK(z) -{ 1 }-> 1 + A__LENGTH(1 + mark(z012) + z17) + MARK(1 + z012 + z17) :|: z = 1 + (1 + z012 + z17), z17 >= 0, z012 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(1 + 0 + 3) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__AND(a__take(mark(z06), mark(z13)), z1) + MARK(1 + z06 + z13) :|: z1 >= 0, z = 1 + (1 + z06 + z13) + z1, z06 >= 0, z13 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__length(mark(z05)), z1) + MARK(1 + z05) :|: z1 >= 0, z = 1 + (1 + z05) + z1, z05 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__and(mark(z04), z12), z1) + MARK(1 + z04 + z12) :|: z04 >= 0, z = 1 + (1 + z04 + z12) + z1, z1 >= 0, z12 >= 0 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(z08), z1) + MARK(1 + z08) :|: z08 >= 0, z1 >= 0, z = 1 + (1 + z08) + z1 MARK(z) -{ 1 }-> 1 + A__AND(1 + mark(z07) + z14, z1) + MARK(1 + z07 + z14) :|: z1 >= 0, z07 >= 0, z = 1 + (1 + z07 + z14) + z1, z14 >= 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__take(mark(z0126), mark(z175))) :|: z = 1 + z0 + (1 + z0126 + z175), z0 >= 0, z175 >= 0, z0126 >= 0 a__length(z) -{ 0 }-> 1 + a__length(a__length(mark(z0125))) :|: z = 1 + z0 + (1 + z0125), z0 >= 0, z0125 >= 0 a__length(z) -{ 0 }-> 1 + a__length(a__and(mark(z0124), z174)) :|: z = 1 + z0 + (1 + z0124 + z174), z0 >= 0, z0124 >= 0, z174 >= 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(z0128)) :|: z0 >= 0, z0128 >= 0, z = 1 + z0 + (1 + z0128) a__length(z) -{ 0 }-> 1 + a__length(1 + mark(z0127) + z176) :|: z = 1 + z0 + (1 + z0127 + z176), z0 >= 0, z0127 >= 0, z176 >= 0 a__length(z) -{ 0 }-> 1 + a__length(1 + 0 + 3) :|: z = 1 + z0 + 3, z0 >= 0 a__take(z, z') -{ 0 }-> 1 :|: z0 >= 0, z = 0, z' = z0 a__take(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__take(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__take(z, z') -{ 0 }-> 1 + mark(z1) + (1 + z0 + z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 a__zeros -{ 0 }-> 3 :|: a__zeros -{ 0 }-> 0 :|: a__zeros -{ 0 }-> 1 + 0 + 3 :|: mark(z) -{ 0 }-> a__take(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__length(a__take(mark(z0136), mark(z181))) :|: z0136 >= 0, z181 >= 0, z = 1 + (1 + z0136 + z181) mark(z) -{ 0 }-> a__length(a__length(mark(z0135))) :|: z = 1 + (1 + z0135), z0135 >= 0 mark(z) -{ 0 }-> a__length(a__and(mark(z0134), z180)) :|: z = 1 + (1 + z0134 + z180), z0134 >= 0, z180 >= 0 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(z0138)) :|: z = 1 + (1 + z0138), z0138 >= 0 mark(z) -{ 0 }-> a__length(1 + mark(z0137) + z182) :|: z182 >= 0, z0137 >= 0, z = 1 + (1 + z0137 + z182) mark(z) -{ 0 }-> a__length(1 + 0 + 3) :|: z = 1 + 3 mark(z) -{ 0 }-> a__and(a__take(mark(z0131), mark(z178)), z1) :|: z1 >= 0, z = 1 + (1 + z0131 + z178) + z1, z0131 >= 0, z178 >= 0 mark(z) -{ 0 }-> a__and(a__length(mark(z0130)), z1) :|: z = 1 + (1 + z0130) + z1, z1 >= 0, z0130 >= 0 mark(z) -{ 0 }-> a__and(a__and(mark(z0129), z177), z1) :|: z1 >= 0, z0129 >= 0, z = 1 + (1 + z0129 + z177) + z1, z177 >= 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(z0133), z1) :|: z1 >= 0, z0133 >= 0, z = 1 + (1 + z0133) + z1 mark(z) -{ 0 }-> a__and(1 + mark(z0132) + z179, z1) :|: z0132 >= 0, z1 >= 0, z179 >= 0, z = 1 + (1 + z0132 + z179) + z1 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__take(mark(z01), mark(z1''))) + MARK(1 + z01 + z1'') :|: z = 1 + z0 + (1 + z01 + z1''), z01 >= 0, z0 >= 0, z1'' >= 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(z03)) + MARK(1 + z03) :|: z = 1 + z0 + (1 + z03), z0 >= 0, z03 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(1 + mark(z02) + z11) + MARK(1 + z02 + z11) :|: z = 1 + z0 + (1 + z02 + z11), z11 >= 0, z02 >= 0, z0 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__LENGTH(1 + 0 + 3) + MARK(3) :|: z - 4 >= 0 A__TAKE(z, z') -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 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__TAKE(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__LENGTH(a__take(mark(z011), mark(z16))) + MARK(1 + z011 + z16) :|: z011 >= 0, z = 1 + (1 + z011 + z16), z16 >= 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(z09), z15)) + MARK(1 + z09 + z15) :|: z15 >= 0, z09 >= 0, z = 1 + (1 + z09 + z15) 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(z012) + z17) + MARK(1 + z012 + z17) :|: z = 1 + (1 + z012 + z17), z17 >= 0, z012 >= 0 MARK(z) -{ 1 }-> 1 + A__LENGTH(1 + 0 + 3) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__AND(a__take(mark(z06), mark(z13)), z1) + MARK(1 + z06 + z13) :|: z1 >= 0, z = 1 + (1 + z06 + z13) + z1, z06 >= 0, z13 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__length(mark(z05)), z1) + MARK(1 + z05) :|: z1 >= 0, z = 1 + (1 + z05) + z1, z05 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__and(mark(z04), z12), z1) + MARK(1 + z04 + z12) :|: z04 >= 0, z = 1 + (1 + z04 + z12) + z1, z1 >= 0, z12 >= 0 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(z08), z1) + MARK(1 + z08) :|: z08 >= 0, z1 >= 0, z = 1 + (1 + z08) + z1 MARK(z) -{ 1 }-> 1 + A__AND(1 + mark(z07) + z14, z1) + MARK(1 + z07 + z14) :|: z1 >= 0, z07 >= 0, z = 1 + (1 + z07 + z14) + z1, z14 >= 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__take(mark(z0126), mark(z175))) :|: z = 1 + z0 + (1 + z0126 + z175), z0 >= 0, z175 >= 0, z0126 >= 0 a__length(z) -{ 0 }-> 1 + a__length(a__length(mark(z0125))) :|: z = 1 + z0 + (1 + z0125), z0 >= 0, z0125 >= 0 a__length(z) -{ 0 }-> 1 + a__length(a__and(mark(z0124), z174)) :|: z = 1 + z0 + (1 + z0124 + z174), z0 >= 0, z0124 >= 0, z174 >= 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(z0128)) :|: z0 >= 0, z0128 >= 0, z = 1 + z0 + (1 + z0128) a__length(z) -{ 0 }-> 1 + a__length(1 + mark(z0127) + z176) :|: z = 1 + z0 + (1 + z0127 + z176), z0 >= 0, z0127 >= 0, z176 >= 0 a__length(z) -{ 0 }-> 1 + a__length(1 + 0 + 3) :|: z - 4 >= 0 a__take(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0 a__take(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__take(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__take(z, z') -{ 0 }-> 1 + mark(z1) + (1 + (z - 1) + z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 a__zeros -{ 0 }-> 3 :|: a__zeros -{ 0 }-> 0 :|: a__zeros -{ 0 }-> 1 + 0 + 3 :|: mark(z) -{ 0 }-> a__take(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__length(a__take(mark(z0136), mark(z181))) :|: z0136 >= 0, z181 >= 0, z = 1 + (1 + z0136 + z181) mark(z) -{ 0 }-> a__length(a__length(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__length(a__and(mark(z0134), z180)) :|: z = 1 + (1 + z0134 + z180), z0134 >= 0, z180 >= 0 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(z0137) + z182) :|: z182 >= 0, z0137 >= 0, z = 1 + (1 + z0137 + z182) mark(z) -{ 0 }-> a__length(1 + 0 + 3) :|: z = 1 + 3 mark(z) -{ 0 }-> a__and(a__take(mark(z0131), mark(z178)), z1) :|: z1 >= 0, z = 1 + (1 + z0131 + z178) + z1, z0131 >= 0, z178 >= 0 mark(z) -{ 0 }-> a__and(a__length(mark(z0130)), z1) :|: z = 1 + (1 + z0130) + z1, z1 >= 0, z0130 >= 0 mark(z) -{ 0 }-> a__and(a__and(mark(z0129), z177), z1) :|: z1 >= 0, z0129 >= 0, z = 1 + (1 + z0129 + z177) + z1, z177 >= 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(z0133), z1) :|: z1 >= 0, z0133 >= 0, z = 1 + (1 + z0133) + z1 mark(z) -{ 0 }-> a__and(1 + mark(z0132) + z179, z1) :|: z0132 >= 0, z1 >= 0, z179 >= 0, z = 1 + (1 + z0132 + z179) + z1 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] a__take(v0, v1) -> null_a__take [0] mark(v0) -> null_mark [0] A__AND(v0, v1) -> null_A__AND [0] A__LENGTH(v0) -> null_A__LENGTH [0] A__TAKE(v0, v1) -> null_A__TAKE [0] MARK(v0) -> null_MARK [0] And the following fresh constants: null_a__zeros, null_a__and, null_a__length, null_a__take, null_mark, null_A__AND, null_A__LENGTH, null_A__TAKE, 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] A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) [1] MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) [1] MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c15(MARK(z0)) [1] MARK(s(z0)) -> c19(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] a__take(0, z0) -> nil [0] a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) [0] a__take(z0, z1) -> take(z0, z1) [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(take(z0, z1)) -> a__take(mark(z0), mark(z1)) [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] a__take(v0, v1) -> null_a__take [0] mark(v0) -> null_mark [0] A__AND(v0, v1) -> null_A__AND [0] A__LENGTH(v0) -> null_A__LENGTH [0] A__TAKE(v0, v1) -> null_A__TAKE [0] MARK(v0) -> null_MARK [0] The TRS has the following type information: A__AND :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> c2:null_A__AND tt :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark c2 :: c11:c12:c13:c14:c15:c19:null_MARK -> c2:null_A__AND MARK :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> c11:c12:c13:c14:c15:c19:null_MARK A__LENGTH :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> c5:null_A__LENGTH cons :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark c5 :: c5:null_A__LENGTH -> c11:c12:c13:c14:c15:c19:null_MARK -> c5:null_A__LENGTH mark :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark A__TAKE :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> c8:null_A__TAKE s :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark c8 :: c11:c12:c13:c14:c15:c19:null_MARK -> c8:null_A__TAKE and :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark c11 :: c2:null_A__AND -> c11:c12:c13:c14:c15:c19:null_MARK -> c11:c12:c13:c14:c15:c19:null_MARK length :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark c12 :: c5:null_A__LENGTH -> c11:c12:c13:c14:c15:c19:null_MARK -> c11:c12:c13:c14:c15:c19:null_MARK take :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark c13 :: c8:null_A__TAKE -> c11:c12:c13:c14:c15:c19:null_MARK -> c11:c12:c13:c14:c15:c19:null_MARK c14 :: c8:null_A__TAKE -> c11:c12:c13:c14:c15:c19:null_MARK -> c11:c12:c13:c14:c15:c19:null_MARK c15 :: c11:c12:c13:c14:c15:c19:null_MARK -> c11:c12:c13:c14:c15:c19:null_MARK c19 :: c11:c12:c13:c14:c15:c19:null_MARK -> c11:c12:c13:c14:c15:c19:null_MARK a__zeros :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark 0 :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark zeros :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark a__and :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark a__length :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark nil :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark a__take :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark -> tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark null_a__zeros :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark null_a__and :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark null_a__length :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark null_a__take :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark null_mark :: tt:cons:s:and:length:take:0:zeros:nil:null_a__zeros:null_a__and:null_a__length:null_a__take:null_mark null_A__AND :: c2:null_A__AND null_A__LENGTH :: c5:null_A__LENGTH null_A__TAKE :: c8:null_A__TAKE null_MARK :: c11:c12:c13:c14:c15:c19: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_a__take => 0 null_mark => 0 null_A__AND => 0 null_A__LENGTH => 0 null_A__TAKE => 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 A__TAKE(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__TAKE(z, z') -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 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__TAKE(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 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__take(z, z') -{ 0 }-> 1 :|: z0 >= 0, z = 0, z' = z0 a__take(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__take(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__take(z, z') -{ 0 }-> 1 + mark(z1) + (1 + z0 + z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 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__take(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c11_2, c12_2, c13_2, c14_2, c15_1, c19_1, c5_2 ---------------------------------------- (51) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: A__LENGTH(cons(x0, tt)) -> c5(A__LENGTH(tt), MARK(tt)) A__LENGTH(cons(x0, 0)) -> c5(A__LENGTH(0), MARK(0)) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c11_2, c12_2, c13_2, c14_2, c15_1, c19_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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c11_2, c12_2, c13_2, c14_2, c15_1, c19_1, c5_2, c5_1 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) by MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(cons(z0, z1), x1)) -> c11(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(0, x1)) -> c11(A__AND(0, x1), MARK(0)) MARK(and(tt, x1)) -> c11(A__AND(tt, x1), MARK(tt)) MARK(and(nil, x1)) -> c11(A__AND(nil, x1), MARK(nil)) MARK(and(s(z0), x1)) -> c11(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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(cons(z0, z1), x1)) -> c11(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(0, x1)) -> c11(A__AND(0, x1), MARK(0)) MARK(and(tt, x1)) -> c11(A__AND(tt, x1), MARK(tt)) MARK(and(nil, x1)) -> c11(A__AND(nil, x1), MARK(nil)) MARK(and(s(z0), x1)) -> c11(A__AND(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(cons(z0, z1), x1)) -> c11(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(0, x1)) -> c11(A__AND(0, x1), MARK(0)) MARK(and(tt, x1)) -> c11(A__AND(tt, x1), MARK(tt)) MARK(and(nil, x1)) -> c11(A__AND(nil, x1), MARK(nil)) MARK(and(s(z0), x1)) -> c11(A__AND(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c12_2, c13_2, c14_2, c15_1, c19_1, c5_2, c5_1, c11_2 ---------------------------------------- (57) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(and(0, x1)) -> c11(A__AND(0, x1), MARK(0)) MARK(and(nil, x1)) -> c11(A__AND(nil, x1), MARK(nil)) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(cons(z0, z1), x1)) -> c11(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c11(A__AND(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(cons(z0, z1), x1)) -> c11(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c11(A__AND(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c12_2, c13_2, c14_2, c15_1, c19_1, c5_2, c5_1, c11_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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c12_2, c13_2, c14_2, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1 ---------------------------------------- (61) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) by MARK(length(zeros)) -> c12(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(0)) -> c12(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c12(A__LENGTH(tt), MARK(tt)) MARK(length(nil)) -> c12(A__LENGTH(nil), MARK(nil)) MARK(length(s(z0))) -> c12(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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(0)) -> c12(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c12(A__LENGTH(tt), MARK(tt)) MARK(length(nil)) -> c12(A__LENGTH(nil), MARK(nil)) MARK(length(s(z0))) -> c12(A__LENGTH(s(mark(z0))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(0)) -> c12(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c12(A__LENGTH(tt), MARK(tt)) MARK(length(nil)) -> c12(A__LENGTH(nil), MARK(nil)) MARK(length(s(z0))) -> c12(A__LENGTH(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c13_2, c14_2, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2 ---------------------------------------- (63) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(length(nil)) -> c12(A__LENGTH(nil), MARK(nil)) MARK(length(0)) -> c12(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c12(A__LENGTH(tt), MARK(tt)) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(A__LENGTH(s(mark(z0))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(A__LENGTH(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c13_2, c14_2, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c13_2, c14_2, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1 ---------------------------------------- (67) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) by MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c13(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c13(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, nil)) -> c13(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(x0, s(z0))) -> c13(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c13(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c13(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(tt, x1)) -> c13(A__TAKE(tt, mark(x1)), MARK(tt)) MARK(take(nil, x1)) -> c13(A__TAKE(nil, mark(x1)), MARK(nil)) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c13(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c13(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, nil)) -> c13(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(x0, s(z0))) -> c13(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c13(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c13(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(tt, x1)) -> c13(A__TAKE(tt, mark(x1)), MARK(tt)) MARK(take(nil, x1)) -> c13(A__TAKE(nil, mark(x1)), MARK(nil)) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c13(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c13(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, nil)) -> c13(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(x0, s(z0))) -> c13(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c13(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c13(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(tt, x1)) -> c13(A__TAKE(tt, mark(x1)), MARK(tt)) MARK(take(nil, x1)) -> c13(A__TAKE(nil, mark(x1)), MARK(nil)) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c14_2, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2 ---------------------------------------- (69) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(nil, x1)) -> c13(A__TAKE(nil, mark(x1)), MARK(nil)) MARK(take(0, x1)) -> c13(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(tt, x1)) -> c13(A__TAKE(tt, mark(x1)), MARK(tt)) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c13(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c13(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, nil)) -> c13(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(x0, s(z0))) -> c13(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c13(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c13(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c13(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, nil)) -> c13(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(x0, s(z0))) -> c13(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c13(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c14_2, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2 ---------------------------------------- (71) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c14_2, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1 ---------------------------------------- (73) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) by MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, 0)) -> c14(A__TAKE(mark(x0), 0), MARK(0)) MARK(take(x0, tt)) -> c14(A__TAKE(mark(x0), tt), MARK(tt)) MARK(take(x0, nil)) -> c14(A__TAKE(mark(x0), nil), MARK(nil)) MARK(take(x0, s(z0))) -> c14(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c14(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c14(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c14(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c14(A__TAKE(nil, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, 0)) -> c14(A__TAKE(mark(x0), 0), MARK(0)) MARK(take(x0, tt)) -> c14(A__TAKE(mark(x0), tt), MARK(tt)) MARK(take(x0, nil)) -> c14(A__TAKE(mark(x0), nil), MARK(nil)) MARK(take(x0, s(z0))) -> c14(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c14(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c14(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c14(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c14(A__TAKE(nil, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, 0)) -> c14(A__TAKE(mark(x0), 0), MARK(0)) MARK(take(x0, tt)) -> c14(A__TAKE(mark(x0), tt), MARK(tt)) MARK(take(x0, nil)) -> c14(A__TAKE(mark(x0), nil), MARK(nil)) MARK(take(x0, s(z0))) -> c14(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c14(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c14(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c14(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c14(A__TAKE(nil, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2 ---------------------------------------- (75) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(x0, nil)) -> c14(A__TAKE(mark(x0), nil), MARK(nil)) MARK(take(x0, tt)) -> c14(A__TAKE(mark(x0), tt), MARK(tt)) MARK(take(x0, 0)) -> c14(A__TAKE(mark(x0), 0), MARK(0)) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c14(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c14(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c14(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c14(A__TAKE(nil, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c14(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c14(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c14(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c14(A__TAKE(nil, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2 ---------------------------------------- (77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (79) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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))) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (83) 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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)))) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) 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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (87) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) by A__LENGTH(cons(x0, take(x1, x2))) -> c5(A__LENGTH(take(mark(x1), mark(x2))), MARK(take(x1, x2))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, x2))) -> c5(A__LENGTH(take(mark(x1), mark(x2))), MARK(take(x1, x2))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, x2))) -> c5(A__LENGTH(take(mark(x1), mark(x2))), MARK(take(x1, x2))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (89) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (91) 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)) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) 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)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) 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, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (93) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(zeros)) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) 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, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (95) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) by MARK(and(and(x0, z1), x2)) -> c11(A__AND(and(mark(x0), z1), x2), MARK(and(x0, z1))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2), MARK(and(0, x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2), MARK(and(nil, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(x0, z1), x2)) -> c11(A__AND(and(mark(x0), z1), x2), MARK(and(x0, z1))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2), MARK(and(0, x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2), MARK(and(nil, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(x0, z1), x2)) -> c11(A__AND(and(mark(x0), z1), x2), MARK(and(x0, z1))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2), MARK(and(0, x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2), MARK(and(nil, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(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, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (97) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (99) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) by MARK(and(length(x0), x1)) -> c11(A__AND(length(mark(x0)), x1), MARK(length(x0))) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1), MARK(length(0))) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1), MARK(length(tt))) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1), MARK(length(nil))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(x0), x1)) -> c11(A__AND(length(mark(x0)), x1), MARK(length(x0))) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1), MARK(length(0))) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1), MARK(length(tt))) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1), MARK(length(nil))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(x0), x1)) -> c11(A__AND(length(mark(x0)), x1), MARK(length(x0))) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1), MARK(length(0))) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1), MARK(length(tt))) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1), MARK(length(nil))) MARK(and(length(s(z0)), x1)) -> c11(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, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (101) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (103) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) by MARK(and(take(x0, x1), x2)) -> c11(A__AND(take(mark(x0), mark(x1)), x2), MARK(take(x0, x1))) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) 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mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, x1), x2)) -> c11(A__AND(take(mark(x0), mark(x1)), x2), MARK(take(x0, x1))) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (105) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (107) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) by MARK(and(zeros, x0)) -> c11(A__AND(cons(0, zeros), x0)) MARK(and(zeros, x0)) -> c11(A__AND(zeros, x0)) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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)), 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c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) MARK(and(zeros, x0)) -> c11(A__AND(cons(0, zeros), x0)) MARK(and(zeros, x0)) -> c11(A__AND(zeros, x0)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (109) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(and(zeros, x0)) -> c11(A__AND(zeros, x0)) MARK(and(zeros, x0)) -> c11(A__AND(cons(0, zeros), x0)) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (111) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) by MARK(length(and(x0, z1))) -> c12(A__LENGTH(and(mark(x0), z1)), MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1)), MARK(and(zeros, x1))) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1)), MARK(and(0, x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1)), MARK(and(nil, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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))) 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c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1)), MARK(and(0, x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1)), MARK(and(nil, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), 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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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(x0, z1))) -> c12(A__LENGTH(and(mark(x0), z1)), MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1)), MARK(and(zeros, x1))) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1)), MARK(and(0, x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1)), MARK(and(nil, x1))) MARK(length(and(s(z0), x1))) -> c12(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, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (115) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) 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MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) by MARK(length(length(x0))) -> c12(A__LENGTH(length(mark(x0))), MARK(length(x0))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0)), MARK(length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt)), MARK(length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil)), MARK(length(nil))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) 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c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(x0))) -> c12(A__LENGTH(length(mark(x0))), MARK(length(x0))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0)), MARK(length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt)), MARK(length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil)), MARK(length(nil))) MARK(length(length(s(z0)))) -> c12(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, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (119) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (121) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) by MARK(length(take(x0, x1))) -> c12(A__LENGTH(take(mark(x0), mark(x1))), MARK(take(x0, x1))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), 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c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, 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-> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, x1))) -> c12(A__LENGTH(take(mark(x0), mark(x1))), MARK(take(x0, x1))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (123) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), 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c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (125) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) by MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(length(zeros)) -> c12(A__LENGTH(zeros)) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, 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c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(length(zeros)) -> c12(A__LENGTH(zeros)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (127) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(length(zeros)) -> c12(A__LENGTH(zeros)) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, 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MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (129) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) by MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), zeros), MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros), MARK(zeros)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(cons(z0, z1), zeros)) -> c13(A__TAKE(cons(mark(z0), z1), a__zeros), MARK(cons(z0, z1))) MARK(take(0, zeros)) -> c13(A__TAKE(0, a__zeros), MARK(0)) MARK(take(tt, zeros)) -> c13(A__TAKE(tt, a__zeros), MARK(tt)) MARK(take(nil, zeros)) -> c13(A__TAKE(nil, a__zeros), MARK(nil)) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) 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MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, 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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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), zeros), MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros), MARK(zeros)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(cons(z0, z1), zeros)) -> c13(A__TAKE(cons(mark(z0), z1), a__zeros), MARK(cons(z0, z1))) MARK(take(0, zeros)) -> c13(A__TAKE(0, a__zeros), MARK(0)) MARK(take(tt, zeros)) -> c13(A__TAKE(tt, a__zeros), MARK(tt)) MARK(take(nil, zeros)) -> c13(A__TAKE(nil, a__zeros), MARK(nil)) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (131) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(nil, zeros)) -> c13(A__TAKE(nil, a__zeros), MARK(nil)) MARK(take(0, zeros)) -> c13(A__TAKE(0, a__zeros), MARK(0)) MARK(take(tt, zeros)) -> c13(A__TAKE(tt, a__zeros), MARK(tt)) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> 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MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), zeros), MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros), MARK(zeros)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(cons(z0, z1), zeros)) -> c13(A__TAKE(cons(mark(z0), z1), a__zeros), MARK(cons(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (133) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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)))) 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MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (135) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) by MARK(take(x0, and(x1, z1))) -> c13(A__TAKE(mark(x0), and(mark(x1), z1)), MARK(x0)) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(zeros)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(A__TAKE(cons(mark(z0), z1), a__and(mark(x1), x2)), MARK(cons(z0, z1))) MARK(take(0, and(x1, x2))) -> c13(A__TAKE(0, a__and(mark(x1), x2)), MARK(0)) MARK(take(tt, and(x1, x2))) -> c13(A__TAKE(tt, a__and(mark(x1), x2)), MARK(tt)) MARK(take(nil, and(x1, x2))) -> c13(A__TAKE(nil, a__and(mark(x1), x2)), MARK(nil)) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), 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MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(x1, z1))) -> c13(A__TAKE(mark(x0), and(mark(x1), z1)), MARK(x0)) 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c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(x1, z1))) -> c13(A__TAKE(mark(x0), and(mark(x1), z1)), MARK(x0)) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(zeros)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(A__TAKE(cons(mark(z0), z1), a__and(mark(x1), x2)), MARK(cons(z0, z1))) MARK(take(0, and(x1, x2))) -> c13(A__TAKE(0, a__and(mark(x1), x2)), MARK(0)) MARK(take(tt, and(x1, x2))) -> c13(A__TAKE(tt, a__and(mark(x1), x2)), MARK(tt)) MARK(take(nil, and(x1, x2))) -> c13(A__TAKE(nil, a__and(mark(x1), x2)), MARK(nil)) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (137) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(0, and(x1, x2))) -> c13(A__TAKE(0, a__and(mark(x1), x2)), MARK(0)) MARK(take(nil, and(x1, x2))) -> c13(A__TAKE(nil, a__and(mark(x1), x2)), MARK(nil)) MARK(take(tt, and(x1, x2))) -> c13(A__TAKE(tt, a__and(mark(x1), x2)), MARK(tt)) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> 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c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) 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MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(x1, z1))) -> c13(A__TAKE(mark(x0), and(mark(x1), z1)), MARK(x0)) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, 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MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(x1, z1))) -> c13(A__TAKE(mark(x0), and(mark(x1), z1)), MARK(x0)) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(zeros)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(A__TAKE(cons(mark(z0), z1), a__and(mark(x1), x2)), MARK(cons(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (139) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, 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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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (141) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) by MARK(take(x0, length(x1))) -> c13(A__TAKE(mark(x0), length(mark(x1))), MARK(x0)) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1))), MARK(zeros)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(cons(z0, z1), length(x1))) -> c13(A__TAKE(cons(mark(z0), z1), a__length(mark(x1))), MARK(cons(z0, z1))) MARK(take(0, length(x1))) -> c13(A__TAKE(0, a__length(mark(x1))), MARK(0)) MARK(take(tt, length(x1))) -> c13(A__TAKE(tt, a__length(mark(x1))), MARK(tt)) MARK(take(nil, length(x1))) -> c13(A__TAKE(nil, a__length(mark(x1))), MARK(nil)) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), 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c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(x1))) -> c13(A__TAKE(mark(x0), length(mark(x1))), MARK(x0)) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1))), MARK(zeros)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(cons(z0, z1), length(x1))) -> c13(A__TAKE(cons(mark(z0), z1), a__length(mark(x1))), MARK(cons(z0, z1))) MARK(take(0, length(x1))) -> c13(A__TAKE(0, a__length(mark(x1))), MARK(0)) MARK(take(tt, length(x1))) -> c13(A__TAKE(tt, a__length(mark(x1))), MARK(tt)) MARK(take(nil, length(x1))) -> c13(A__TAKE(nil, a__length(mark(x1))), MARK(nil)) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (143) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(nil, length(x1))) -> c13(A__TAKE(nil, a__length(mark(x1))), MARK(nil)) MARK(take(tt, length(x1))) -> c13(A__TAKE(tt, a__length(mark(x1))), MARK(tt)) MARK(take(0, length(x1))) -> c13(A__TAKE(0, a__length(mark(x1))), MARK(0)) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) 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c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(cons(z0, z1), length(x1))) -> c13(A__TAKE(cons(mark(z0), z1), a__length(mark(x1))), MARK(cons(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, 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x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(x1))) -> c13(A__TAKE(mark(x0), length(mark(x1))), MARK(x0)) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1))), MARK(zeros)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(cons(z0, z1), length(x1))) -> c13(A__TAKE(cons(mark(z0), z1), a__length(mark(x1))), MARK(cons(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (145) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) 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MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), 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c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (147) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) by MARK(take(x0, take(x1, x2))) -> c13(A__TAKE(mark(x0), take(mark(x1), mark(x2))), MARK(x0)) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(zeros)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(A__TAKE(cons(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(take(0, take(x1, x2))) -> c13(A__TAKE(0, a__take(mark(x1), mark(x2))), MARK(0)) MARK(take(tt, take(x1, x2))) -> c13(A__TAKE(tt, a__take(mark(x1), mark(x2))), MARK(tt)) MARK(take(nil, take(x1, x2))) -> c13(A__TAKE(nil, a__take(mark(x1), mark(x2))), MARK(nil)) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, x2))) -> c13(A__TAKE(mark(x0), take(mark(x1), mark(x2))), MARK(x0)) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(zeros)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(A__TAKE(cons(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(take(0, take(x1, x2))) -> c13(A__TAKE(0, a__take(mark(x1), mark(x2))), MARK(0)) MARK(take(tt, take(x1, x2))) -> c13(A__TAKE(tt, a__take(mark(x1), mark(x2))), MARK(tt)) MARK(take(nil, take(x1, x2))) -> c13(A__TAKE(nil, a__take(mark(x1), mark(x2))), MARK(nil)) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), 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a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, x2))) -> c13(A__TAKE(mark(x0), take(mark(x1), mark(x2))), MARK(x0)) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(zeros)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(A__TAKE(cons(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(take(0, take(x1, x2))) -> c13(A__TAKE(0, a__take(mark(x1), mark(x2))), MARK(0)) MARK(take(tt, take(x1, x2))) -> c13(A__TAKE(tt, a__take(mark(x1), mark(x2))), MARK(tt)) MARK(take(nil, take(x1, x2))) -> c13(A__TAKE(nil, a__take(mark(x1), mark(x2))), MARK(nil)) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (149) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(tt, take(x1, x2))) -> c13(A__TAKE(tt, a__take(mark(x1), mark(x2))), MARK(tt)) MARK(take(nil, take(x1, x2))) -> c13(A__TAKE(nil, a__take(mark(x1), mark(x2))), MARK(nil)) MARK(take(0, take(x1, x2))) -> c13(A__TAKE(0, a__take(mark(x1), mark(x2))), MARK(0)) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) 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c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, x2))) -> c13(A__TAKE(mark(x0), take(mark(x1), mark(x2))), MARK(x0)) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(zeros)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(A__TAKE(cons(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (151) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) 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MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) 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a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), 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c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (153) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) by MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(zeros)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(A__TAKE(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) MARK(take(0, cons(x1, x2))) -> c13(A__TAKE(0, cons(mark(x1), x2)), MARK(0)) MARK(take(tt, cons(x1, x2))) -> c13(A__TAKE(tt, cons(mark(x1), x2)), MARK(tt)) MARK(take(nil, cons(x1, x2))) -> c13(A__TAKE(nil, cons(mark(x1), x2)), MARK(nil)) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) 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c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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, 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c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(zeros)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(A__TAKE(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) MARK(take(0, cons(x1, x2))) -> c13(A__TAKE(0, cons(mark(x1), x2)), MARK(0)) MARK(take(tt, cons(x1, x2))) -> c13(A__TAKE(tt, cons(mark(x1), x2)), MARK(tt)) MARK(take(nil, cons(x1, x2))) -> c13(A__TAKE(nil, cons(mark(x1), x2)), MARK(nil)) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (155) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(0, cons(x1, x2))) -> c13(A__TAKE(0, cons(mark(x1), x2)), MARK(0)) MARK(take(nil, cons(x1, x2))) -> c13(A__TAKE(nil, cons(mark(x1), x2)), MARK(nil)) MARK(take(tt, cons(x1, x2))) -> c13(A__TAKE(tt, cons(mark(x1), x2)), MARK(tt)) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 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c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> 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x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(zeros)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(A__TAKE(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (157) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> 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c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (159) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) by MARK(take(and(x0, x1), zeros)) -> c13(A__TAKE(a__and(mark(x0), x1), a__zeros), MARK(and(x0, x1))) MARK(take(and(x0, x1), and(z0, z1))) -> c13(A__TAKE(a__and(mark(x0), x1), a__and(mark(z0), z1)), MARK(and(x0, x1))) MARK(take(and(x0, x1), length(z0))) -> c13(A__TAKE(a__and(mark(x0), x1), a__length(mark(z0))), MARK(and(x0, x1))) MARK(take(and(x0, x1), take(z0, z1))) -> c13(A__TAKE(a__and(mark(x0), x1), a__take(mark(z0), mark(z1))), MARK(and(x0, x1))) MARK(take(and(x0, x1), cons(z0, z1))) -> c13(A__TAKE(a__and(mark(x0), x1), cons(mark(z0), z1)), MARK(and(x0, x1))) MARK(take(and(x0, x1), 0)) -> c13(A__TAKE(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(A__TAKE(a__and(mark(x0), x1), tt), MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(A__TAKE(a__and(mark(x0), x1), nil), MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(A__TAKE(a__and(mark(x0), x1), s(mark(z0))), MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(A__TAKE(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(and(zeros, x1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2)), MARK(and(0, x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2)), MARK(and(nil, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), 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MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), 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length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(x0, x1), 0)) -> c13(A__TAKE(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(A__TAKE(a__and(mark(x0), x1), tt), MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(A__TAKE(a__and(mark(x0), x1), nil), MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(A__TAKE(a__and(mark(x0), x1), s(mark(z0))), MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(A__TAKE(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(and(zeros, x1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2)), MARK(and(0, x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2)), MARK(and(nil, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (161) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 8 trailing tuple parts ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) 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x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (163) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) by MARK(take(length(x0), zeros)) -> c13(A__TAKE(a__length(mark(x0)), a__zeros), MARK(length(x0))) MARK(take(length(x0), and(z0, z1))) -> c13(A__TAKE(a__length(mark(x0)), a__and(mark(z0), z1)), MARK(length(x0))) MARK(take(length(x0), length(z0))) -> c13(A__TAKE(a__length(mark(x0)), a__length(mark(z0))), MARK(length(x0))) MARK(take(length(x0), take(z0, z1))) -> c13(A__TAKE(a__length(mark(x0)), a__take(mark(z0), mark(z1))), MARK(length(x0))) MARK(take(length(x0), cons(z0, z1))) -> c13(A__TAKE(a__length(mark(x0)), cons(mark(z0), z1)), MARK(length(x0))) MARK(take(length(x0), 0)) -> c13(A__TAKE(a__length(mark(x0)), 0), MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(A__TAKE(a__length(mark(x0)), tt), MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(A__TAKE(a__length(mark(x0)), nil), MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(A__TAKE(a__length(mark(x0)), s(mark(z0))), MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(A__TAKE(length(mark(x0)), mark(x1)), MARK(length(x0))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1)), MARK(length(0))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1)), MARK(length(tt))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1)), MARK(length(nil))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) 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MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(x0), 0)) -> c13(A__TAKE(a__length(mark(x0)), 0), MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(A__TAKE(a__length(mark(x0)), tt), MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(A__TAKE(a__length(mark(x0)), nil), MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(A__TAKE(a__length(mark(x0)), s(mark(z0))), MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(A__TAKE(length(mark(x0)), mark(x1)), MARK(length(x0))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1)), MARK(length(0))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1)), MARK(length(tt))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1)), MARK(length(nil))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, 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c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(x0), 0)) -> c13(A__TAKE(a__length(mark(x0)), 0), MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(A__TAKE(a__length(mark(x0)), tt), MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(A__TAKE(a__length(mark(x0)), nil), MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(A__TAKE(a__length(mark(x0)), s(mark(z0))), MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(A__TAKE(length(mark(x0)), mark(x1)), MARK(length(x0))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1)), MARK(length(0))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1)), MARK(length(tt))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1)), MARK(length(nil))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (165) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 8 trailing tuple parts ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> 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MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (167) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) by MARK(take(take(x0, x1), zeros)) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros), MARK(take(x0, x1))) MARK(take(take(x0, x1), and(z0, z1))) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), a__and(mark(z0), z1)), MARK(take(x0, x1))) MARK(take(take(x0, x1), length(z0))) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), a__length(mark(z0))), MARK(take(x0, x1))) MARK(take(take(x0, x1), take(z0, z1))) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), a__take(mark(z0), mark(z1))), MARK(take(x0, x1))) MARK(take(take(x0, x1), cons(z0, z1))) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(take(x0, x1))) MARK(take(take(x0, x1), 0)) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), 0), MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), tt), MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), nil), MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), s(mark(z0))), MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(A__TAKE(take(mark(x0), mark(x1)), mark(x2)), MARK(take(x0, x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), 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-> c13(A__TAKE(take(mark(x0), mark(x1)), mark(x2)), MARK(take(x0, x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), 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x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, x1), 0)) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), 0), MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), tt), MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), nil), MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), s(mark(z0))), MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(A__TAKE(take(mark(x0), mark(x1)), mark(x2)), MARK(take(x0, x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (169) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, 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MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, 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MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) 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MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) 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c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (171) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) by MARK(take(s(x0), zeros)) -> c13(A__TAKE(s(mark(x0)), a__zeros), MARK(s(x0))) MARK(take(s(x0), and(z0, z1))) -> c13(A__TAKE(s(mark(x0)), a__and(mark(z0), z1)), MARK(s(x0))) MARK(take(s(x0), length(z0))) -> c13(A__TAKE(s(mark(x0)), a__length(mark(z0))), MARK(s(x0))) MARK(take(s(x0), take(z0, z1))) -> c13(A__TAKE(s(mark(x0)), a__take(mark(z0), mark(z1))), MARK(s(x0))) MARK(take(s(x0), cons(z0, z1))) -> c13(A__TAKE(s(mark(x0)), cons(mark(z0), z1)), MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(A__TAKE(s(mark(x0)), 0), MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(A__TAKE(s(mark(x0)), tt), MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(A__TAKE(s(mark(x0)), nil), MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(A__TAKE(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(x0), 0)) -> c13(A__TAKE(s(mark(x0)), 0), MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(A__TAKE(s(mark(x0)), tt), MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(A__TAKE(s(mark(x0)), nil), MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(A__TAKE(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) 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MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(x0), 0)) -> c13(A__TAKE(s(mark(x0)), 0), MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(A__TAKE(s(mark(x0)), tt), MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(A__TAKE(s(mark(x0)), nil), MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(A__TAKE(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (173) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, 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length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (175) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) by MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, and(z0, z1))) -> c13(A__TAKE(a__zeros, a__and(mark(z0), z1))) MARK(take(zeros, length(z0))) -> c13(A__TAKE(a__zeros, a__length(mark(z0)))) MARK(take(zeros, take(z0, z1))) -> c13(A__TAKE(a__zeros, a__take(mark(z0), mark(z1)))) MARK(take(zeros, cons(z0, z1))) -> c13(A__TAKE(a__zeros, cons(mark(z0), z1))) MARK(take(zeros, 0)) -> c13(A__TAKE(a__zeros, 0)) MARK(take(zeros, tt)) -> c13(A__TAKE(a__zeros, tt)) MARK(take(zeros, nil)) -> c13(A__TAKE(a__zeros, nil)) MARK(take(zeros, s(z0))) -> c13(A__TAKE(a__zeros, s(mark(z0)))) MARK(take(zeros, x0)) -> c13(A__TAKE(cons(0, zeros), mark(x0))) MARK(take(zeros, x0)) -> c13(A__TAKE(zeros, mark(x0))) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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))) -> 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a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(zeros, 0)) -> c13(A__TAKE(a__zeros, 0)) MARK(take(zeros, tt)) -> c13(A__TAKE(a__zeros, tt)) MARK(take(zeros, nil)) -> c13(A__TAKE(a__zeros, nil)) MARK(take(zeros, s(z0))) -> c13(A__TAKE(a__zeros, s(mark(z0)))) MARK(take(zeros, x0)) -> c13(A__TAKE(cons(0, zeros), mark(x0))) MARK(take(zeros, x0)) -> c13(A__TAKE(zeros, mark(x0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), 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c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(zeros, 0)) -> c13(A__TAKE(a__zeros, 0)) MARK(take(zeros, tt)) -> c13(A__TAKE(a__zeros, tt)) MARK(take(zeros, nil)) -> c13(A__TAKE(a__zeros, nil)) MARK(take(zeros, s(z0))) -> c13(A__TAKE(a__zeros, s(mark(z0)))) MARK(take(zeros, x0)) -> c13(A__TAKE(cons(0, zeros), mark(x0))) MARK(take(zeros, x0)) -> c13(A__TAKE(zeros, mark(x0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (177) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing nodes: MARK(take(zeros, x0)) -> c13(A__TAKE(cons(0, zeros), mark(x0))) MARK(take(zeros, x0)) -> c13(A__TAKE(zeros, mark(x0))) MARK(take(zeros, nil)) -> c13(A__TAKE(a__zeros, nil)) MARK(take(zeros, s(z0))) -> c13(A__TAKE(a__zeros, s(mark(z0)))) MARK(take(zeros, 0)) -> c13(A__TAKE(a__zeros, 0)) MARK(take(zeros, tt)) -> c13(A__TAKE(a__zeros, tt)) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) 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c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), 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mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> 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-> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (179) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) by MARK(take(x0, and(x1, z1))) -> c14(A__TAKE(mark(x0), and(mark(x1), z1)), MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(and(zeros, x2))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2)), MARK(and(0, x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2)), MARK(and(nil, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(A__TAKE(cons(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(A__TAKE(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(A__TAKE(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(A__TAKE(nil, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> 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length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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), 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take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), 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x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> 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c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(x1, z1))) -> c14(A__TAKE(mark(x0), and(mark(x1), z1)), MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(and(zeros, x2))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2)), MARK(and(0, x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2)), MARK(and(nil, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(A__TAKE(cons(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(A__TAKE(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(A__TAKE(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(A__TAKE(nil, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (181) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 8 trailing tuple parts ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) 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c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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), 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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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, 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MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (183) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) by MARK(take(x0, length(x1))) -> c14(A__TAKE(mark(x0), length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0)), MARK(length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt)), MARK(length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil)), MARK(length(nil))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(cons(z0, z1), length(x1))) -> c14(A__TAKE(cons(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(0, length(x1))) -> c14(A__TAKE(0, a__length(mark(x1))), MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(A__TAKE(tt, a__length(mark(x1))), MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(A__TAKE(nil, a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> 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x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(x1))) -> c14(A__TAKE(mark(x0), length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0)), MARK(length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt)), MARK(length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil)), MARK(length(nil))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(cons(z0, z1), length(x1))) -> c14(A__TAKE(cons(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(0, length(x1))) -> c14(A__TAKE(0, a__length(mark(x1))), MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(A__TAKE(tt, a__length(mark(x1))), MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(A__TAKE(nil, a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, 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MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(x1))) -> c14(A__TAKE(mark(x0), length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0)), MARK(length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt)), MARK(length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil)), MARK(length(nil))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(cons(z0, z1), length(x1))) -> c14(A__TAKE(cons(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(0, length(x1))) -> c14(A__TAKE(0, a__length(mark(x1))), MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(A__TAKE(tt, a__length(mark(x1))), MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(A__TAKE(nil, a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (185) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 8 trailing tuple parts ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 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MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (187) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) by MARK(take(x0, take(x1, x2))) -> c14(A__TAKE(mark(x0), take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(A__TAKE(cons(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(A__TAKE(0, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(A__TAKE(tt, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(A__TAKE(nil, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, 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c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, x2))) -> c14(A__TAKE(mark(x0), take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(A__TAKE(cons(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(A__TAKE(0, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(A__TAKE(tt, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(A__TAKE(nil, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (189) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), 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MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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)))), 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MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, 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c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (191) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) by MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(A__TAKE(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(A__TAKE(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(A__TAKE(tt, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(A__TAKE(nil, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) ---------------------------------------- (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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> 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-> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(A__TAKE(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(A__TAKE(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(A__TAKE(tt, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(A__TAKE(nil, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), 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a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(A__TAKE(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(A__TAKE(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(A__TAKE(tt, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(A__TAKE(nil, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (193) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (194) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, 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z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (195) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) by MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros), MARK(zeros)) MARK(take(zeros, and(z0, z1))) -> c14(A__TAKE(a__zeros, a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(zeros, length(z0))) -> c14(A__TAKE(a__zeros, a__length(mark(z0))), MARK(length(z0))) MARK(take(zeros, take(z0, z1))) -> c14(A__TAKE(a__zeros, a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(zeros, cons(z0, z1))) -> c14(A__TAKE(a__zeros, cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, 0)) -> c14(A__TAKE(a__zeros, 0), MARK(0)) MARK(take(zeros, tt)) -> c14(A__TAKE(a__zeros, tt), MARK(tt)) MARK(take(zeros, nil)) -> c14(A__TAKE(a__zeros, nil), MARK(nil)) MARK(take(zeros, s(z0))) -> c14(A__TAKE(a__zeros, s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x0)) -> c14(A__TAKE(cons(0, zeros), mark(x0)), MARK(x0)) MARK(take(zeros, x0)) -> c14(A__TAKE(zeros, mark(x0)), MARK(x0)) ---------------------------------------- (196) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) 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-> 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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), 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c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) 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c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros), MARK(zeros)) MARK(take(zeros, 0)) -> c14(A__TAKE(a__zeros, 0), MARK(0)) MARK(take(zeros, tt)) -> c14(A__TAKE(a__zeros, tt), MARK(tt)) MARK(take(zeros, nil)) -> c14(A__TAKE(a__zeros, nil), MARK(nil)) MARK(take(zeros, s(z0))) -> c14(A__TAKE(a__zeros, s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x0)) -> c14(A__TAKE(cons(0, zeros), mark(x0)), MARK(x0)) MARK(take(zeros, x0)) -> c14(A__TAKE(zeros, mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (197) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(zeros, nil)) -> c14(A__TAKE(a__zeros, nil), MARK(nil)) MARK(take(zeros, 0)) -> c14(A__TAKE(a__zeros, 0), MARK(0)) MARK(take(zeros, tt)) -> c14(A__TAKE(a__zeros, tt), MARK(tt)) ---------------------------------------- (198) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, 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-> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), 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MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), 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z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros), MARK(zeros)) MARK(take(zeros, s(z0))) -> c14(A__TAKE(a__zeros, s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x0)) -> c14(A__TAKE(cons(0, zeros), mark(x0)), MARK(x0)) MARK(take(zeros, x0)) -> c14(A__TAKE(zeros, mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (199) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (200) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), 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c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, 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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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), 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c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) 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MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, 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z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), 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c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (201) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) by MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros), MARK(zeros)) MARK(take(and(x0, x1), and(z0, z1))) -> c14(A__TAKE(a__and(mark(x0), x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(and(x0, x1), length(z0))) -> c14(A__TAKE(a__and(mark(x0), x1), a__length(mark(z0))), MARK(length(z0))) MARK(take(and(x0, x1), take(z0, z1))) -> c14(A__TAKE(a__and(mark(x0), x1), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(and(x0, x1), cons(z0, z1))) -> c14(A__TAKE(a__and(mark(x0), x1), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(and(x0, x1), 0)) -> c14(A__TAKE(a__and(mark(x0), x1), 0), MARK(0)) MARK(take(and(x0, x1), tt)) -> c14(A__TAKE(a__and(mark(x0), x1), tt), MARK(tt)) MARK(take(and(x0, x1), nil)) -> c14(A__TAKE(a__and(mark(x0), x1), nil), MARK(nil)) MARK(take(and(x0, x1), s(z0))) -> c14(A__TAKE(a__and(mark(x0), x1), s(mark(z0))), MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(A__TAKE(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) ---------------------------------------- (202) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), 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c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) 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cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) 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MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, 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x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros), MARK(zeros)) MARK(take(and(x0, x1), 0)) -> c14(A__TAKE(a__and(mark(x0), x1), 0), MARK(0)) MARK(take(and(x0, x1), tt)) -> c14(A__TAKE(a__and(mark(x0), x1), tt), MARK(tt)) MARK(take(and(x0, x1), nil)) -> c14(A__TAKE(a__and(mark(x0), x1), nil), MARK(nil)) MARK(take(and(x0, x1), s(z0))) -> c14(A__TAKE(a__and(mark(x0), x1), s(mark(z0))), MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(A__TAKE(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), 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c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (203) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(and(x0, x1), nil)) -> c14(A__TAKE(a__and(mark(x0), x1), nil), MARK(nil)) MARK(take(and(x0, x1), tt)) -> c14(A__TAKE(a__and(mark(x0), x1), tt), MARK(tt)) MARK(take(and(x0, x1), 0)) -> c14(A__TAKE(a__and(mark(x0), x1), 0), MARK(0)) ---------------------------------------- (204) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> 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MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), 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MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros), MARK(zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(A__TAKE(a__and(mark(x0), x1), s(mark(z0))), MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(A__TAKE(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, 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c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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))) -> 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c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> 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a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros), MARK(zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(A__TAKE(a__and(mark(x0), x1), s(mark(z0))), MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(A__TAKE(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (205) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (206) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> 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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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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)))) 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c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (207) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) by MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros), MARK(zeros)) MARK(take(length(x0), and(z0, z1))) -> c14(A__TAKE(a__length(mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(length(x0), length(z0))) -> c14(A__TAKE(a__length(mark(x0)), a__length(mark(z0))), MARK(length(z0))) MARK(take(length(x0), take(z0, z1))) -> c14(A__TAKE(a__length(mark(x0)), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(length(x0), cons(z0, z1))) -> c14(A__TAKE(a__length(mark(x0)), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(length(x0), 0)) -> c14(A__TAKE(a__length(mark(x0)), 0), MARK(0)) MARK(take(length(x0), tt)) -> c14(A__TAKE(a__length(mark(x0)), tt), MARK(tt)) MARK(take(length(x0), nil)) -> c14(A__TAKE(a__length(mark(x0)), nil), MARK(nil)) MARK(take(length(x0), s(z0))) -> c14(A__TAKE(a__length(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(A__TAKE(length(mark(x0)), mark(x1)), MARK(x1)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) ---------------------------------------- (208) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), 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c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros), MARK(zeros)) MARK(take(length(x0), 0)) -> c14(A__TAKE(a__length(mark(x0)), 0), MARK(0)) MARK(take(length(x0), tt)) -> c14(A__TAKE(a__length(mark(x0)), tt), MARK(tt)) MARK(take(length(x0), nil)) -> c14(A__TAKE(a__length(mark(x0)), nil), MARK(nil)) MARK(take(length(x0), s(z0))) -> c14(A__TAKE(a__length(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(A__TAKE(length(mark(x0)), mark(x1)), MARK(x1)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (209) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(length(x0), tt)) -> c14(A__TAKE(a__length(mark(x0)), tt), MARK(tt)) MARK(take(length(x0), nil)) -> c14(A__TAKE(a__length(mark(x0)), nil), MARK(nil)) MARK(take(length(x0), 0)) -> c14(A__TAKE(a__length(mark(x0)), 0), MARK(0)) ---------------------------------------- (210) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, 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MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros), MARK(zeros)) MARK(take(length(x0), s(z0))) -> c14(A__TAKE(a__length(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(A__TAKE(length(mark(x0)), mark(x1)), MARK(x1)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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))) -> 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MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros), MARK(zeros)) MARK(take(length(x0), s(z0))) -> c14(A__TAKE(a__length(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(A__TAKE(length(mark(x0)), mark(x1)), MARK(x1)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (211) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (212) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> 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c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> 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MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), 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length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (213) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) by MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros), MARK(zeros)) MARK(take(take(x0, x1), and(z0, z1))) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(take(x0, x1), length(z0))) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__length(mark(z0))), MARK(length(z0))) MARK(take(take(x0, x1), take(z0, z1))) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(take(x0, x1), cons(z0, z1))) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(take(x0, x1), 0)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), 0), MARK(0)) MARK(take(take(x0, x1), tt)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), tt), MARK(tt)) MARK(take(take(x0, x1), nil)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), nil), MARK(nil)) MARK(take(take(x0, x1), s(z0))) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(A__TAKE(take(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) ---------------------------------------- (214) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), 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a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), 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a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros), MARK(zeros)) MARK(take(take(x0, x1), 0)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), 0), MARK(0)) MARK(take(take(x0, x1), tt)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), tt), MARK(tt)) MARK(take(take(x0, x1), nil)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), nil), MARK(nil)) MARK(take(take(x0, x1), s(z0))) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(A__TAKE(take(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (215) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(take(x0, x1), tt)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), tt), MARK(tt)) MARK(take(take(x0, x1), 0)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), 0), MARK(0)) MARK(take(take(x0, x1), nil)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), nil), MARK(nil)) ---------------------------------------- (216) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), 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c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> 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c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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))) 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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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), 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a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros), MARK(zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(A__TAKE(take(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (217) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (218) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), 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c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) 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c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), 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MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (219) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) by MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros), MARK(zeros)) MARK(take(s(x0), and(z0, z1))) -> c14(A__TAKE(s(mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(s(x0), length(z0))) -> c14(A__TAKE(s(mark(x0)), a__length(mark(z0))), MARK(length(z0))) MARK(take(s(x0), take(z0, z1))) -> c14(A__TAKE(s(mark(x0)), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(s(x0), cons(z0, z1))) -> c14(A__TAKE(s(mark(x0)), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(s(x0), 0)) -> c14(A__TAKE(s(mark(x0)), 0), MARK(0)) MARK(take(s(x0), tt)) -> c14(A__TAKE(s(mark(x0)), tt), MARK(tt)) MARK(take(s(x0), nil)) -> c14(A__TAKE(s(mark(x0)), nil), MARK(nil)) MARK(take(s(x0), s(z0))) -> c14(A__TAKE(s(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) ---------------------------------------- (220) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) 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c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros), MARK(zeros)) MARK(take(s(x0), 0)) -> c14(A__TAKE(s(mark(x0)), 0), MARK(0)) MARK(take(s(x0), tt)) -> c14(A__TAKE(s(mark(x0)), tt), MARK(tt)) MARK(take(s(x0), nil)) -> c14(A__TAKE(s(mark(x0)), nil), MARK(nil)) MARK(take(s(x0), s(z0))) -> c14(A__TAKE(s(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (221) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(s(x0), tt)) -> c14(A__TAKE(s(mark(x0)), tt), MARK(tt)) MARK(take(s(x0), nil)) -> c14(A__TAKE(s(mark(x0)), nil), MARK(nil)) MARK(take(s(x0), 0)) -> c14(A__TAKE(s(mark(x0)), 0), MARK(0)) ---------------------------------------- (222) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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))) 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cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros), MARK(zeros)) MARK(take(s(x0), s(z0))) -> c14(A__TAKE(s(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (223) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (224) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), 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MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> 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c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (225) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) by MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), zeros)) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(and(z0, z1), zeros)) -> c14(A__TAKE(a__and(mark(z0), z1), a__zeros)) MARK(take(length(z0), zeros)) -> c14(A__TAKE(a__length(mark(z0)), a__zeros)) MARK(take(take(z0, z1), zeros)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c14(A__TAKE(cons(mark(z0), z1), a__zeros)) MARK(take(0, zeros)) -> c14(A__TAKE(0, a__zeros)) MARK(take(tt, zeros)) -> c14(A__TAKE(tt, a__zeros)) MARK(take(nil, zeros)) -> c14(A__TAKE(nil, a__zeros)) MARK(take(s(z0), zeros)) -> c14(A__TAKE(s(mark(z0)), a__zeros)) ---------------------------------------- (226) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, 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MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), zeros)) MARK(take(cons(z0, z1), zeros)) -> c14(A__TAKE(cons(mark(z0), z1), a__zeros)) MARK(take(0, zeros)) -> c14(A__TAKE(0, a__zeros)) MARK(take(tt, zeros)) -> c14(A__TAKE(tt, a__zeros)) MARK(take(nil, zeros)) -> c14(A__TAKE(nil, a__zeros)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, 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MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, 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a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), zeros)) MARK(take(cons(z0, z1), zeros)) -> c14(A__TAKE(cons(mark(z0), z1), a__zeros)) MARK(take(0, zeros)) -> c14(A__TAKE(0, a__zeros)) MARK(take(tt, zeros)) -> c14(A__TAKE(tt, a__zeros)) MARK(take(nil, zeros)) -> c14(A__TAKE(nil, a__zeros)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (227) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing nodes: MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), zeros)) MARK(take(nil, zeros)) -> c14(A__TAKE(nil, a__zeros)) MARK(take(0, zeros)) -> c14(A__TAKE(0, a__zeros)) MARK(take(tt, zeros)) -> c14(A__TAKE(tt, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c14(A__TAKE(cons(mark(z0), z1), a__zeros)) ---------------------------------------- (228) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, 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c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (229) 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))) ---------------------------------------- (230) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), 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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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), 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MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), 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, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (231) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__LENGTH(cons(x0, and(0, z1))) -> c5(A__LENGTH(and(0, z1))) ---------------------------------------- (232) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), 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c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), 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c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (233) 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))) ---------------------------------------- (234) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), 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c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), 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, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (235) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__LENGTH(cons(x0, and(nil, z1))) -> c5(A__LENGTH(and(nil, z1))) ---------------------------------------- (236) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> 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c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (237) 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))) ---------------------------------------- (238) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) 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MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), 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MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), 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, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (239) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(length(0))) ---------------------------------------- (240) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), 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c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), 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mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (241) 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))) ---------------------------------------- (242) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), 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length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) 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MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(length(tt))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), 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a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), 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, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (243) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(length(tt))) ---------------------------------------- (244) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), 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MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (245) 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))) ---------------------------------------- (246) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), 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c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), 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)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, 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c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), 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, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (247) 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))) ---------------------------------------- (248) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), 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c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) 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-> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, 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c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (249) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) by MARK(and(and(0, z1), x1)) -> c11(A__AND(and(0, z1), x1)) ---------------------------------------- (250) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> 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MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, 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a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), 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c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, 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c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) MARK(and(and(0, z1), x1)) -> c11(A__AND(and(0, z1), x1)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) 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MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) MARK(and(and(0, z1), x1)) -> c11(A__AND(and(0, z1), x1)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (251) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(and(and(0, z1), x1)) -> c11(A__AND(and(0, z1), x1)) ---------------------------------------- (252) 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) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) 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__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(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)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) 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(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), 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(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) 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, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), 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c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (253) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (254) 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] a__take(0, IL) -> nil [1] a__take(s(M), cons(N, IL)) -> cons(mark(N), take(M, IL)) [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(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [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] a__take(X1, X2) -> take(X1, X2) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (255) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (256) 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] a__take(0, IL) -> nil [1] a__take(s(M), cons(N, IL)) -> cons(mark(N), take(M, IL)) [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(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [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] a__take(X1, X2) -> take(X1, X2) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:nil:s:take:and:length cons :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length 0 :: 0:zeros:cons:tt:nil:s:take:and:length zeros :: 0:zeros:cons:tt:nil:s:take:and:length a__and :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length tt :: 0:zeros:cons:tt:nil:s:take:and:length mark :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length a__length :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length nil :: 0:zeros:cons:tt:nil:s:take:and:length s :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length a__take :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length take :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length and :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length length :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length Rewrite Strategy: INNERMOST ---------------------------------------- (257) 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__take_2 a__zeros a__and_2 a__length_1 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (258) 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] a__take(0, IL) -> nil [1] a__take(s(M), cons(N, IL)) -> cons(mark(N), take(M, IL)) [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(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [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] a__take(X1, X2) -> take(X1, X2) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:nil:s:take:and:length cons :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length 0 :: 0:zeros:cons:tt:nil:s:take:and:length zeros :: 0:zeros:cons:tt:nil:s:take:and:length a__and :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length tt :: 0:zeros:cons:tt:nil:s:take:and:length mark :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length a__length :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length nil :: 0:zeros:cons:tt:nil:s:take:and:length s :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length a__take :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length take :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length and :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length length :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length Rewrite Strategy: INNERMOST ---------------------------------------- (259) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (260) 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, take(X1'', X2''))) -> s(a__length(a__take(mark(X1''), mark(X2'')))) [2] a__length(cons(N, cons(X11, X21))) -> s(a__length(cons(mark(X11), X21))) [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] a__take(0, IL) -> nil [1] a__take(s(M), cons(N, IL)) -> cons(mark(N), take(M, IL)) [1] mark(zeros) -> a__zeros [1] mark(and(zeros, X2)) -> a__and(a__zeros, X2) [2] mark(and(and(X12, X22), X2)) -> a__and(a__and(mark(X12), X22), X2) [2] mark(and(length(X3), X2)) -> a__and(a__length(mark(X3)), X2) [2] mark(and(take(X13, X23), X2)) -> a__and(a__take(mark(X13), mark(X23)), X2) [2] mark(and(cons(X14, X24), X2)) -> a__and(cons(mark(X14), X24), 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(X15, X25))) -> a__length(a__and(mark(X15), X25)) [2] mark(length(length(X5))) -> a__length(a__length(mark(X5))) [2] mark(length(take(X16, X26))) -> a__length(a__take(mark(X16), mark(X26))) [2] mark(length(cons(X17, X27))) -> a__length(cons(mark(X17), X27)) [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(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [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] a__take(X1, X2) -> take(X1, X2) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:nil:s:take:and:length cons :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length 0 :: 0:zeros:cons:tt:nil:s:take:and:length zeros :: 0:zeros:cons:tt:nil:s:take:and:length a__and :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length tt :: 0:zeros:cons:tt:nil:s:take:and:length mark :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length a__length :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length nil :: 0:zeros:cons:tt:nil:s:take:and:length s :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length a__take :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length take :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length and :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length length :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length Rewrite Strategy: INNERMOST ---------------------------------------- (261) 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 ---------------------------------------- (262) 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__take(mark(X1''), mark(X2''))) :|: X1'' >= 0, X2'' >= 0, z = 1 + N + (1 + X1'' + X2''), 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(X11) + X21) :|: X11 >= 0, X21 >= 0, z = 1 + N + (1 + X11 + X21), N >= 0 a__take(z, z') -{ 1 }-> 1 :|: z' = IL, z = 0, IL >= 0 a__take(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__take(z, z') -{ 1 }-> 1 + mark(N) + (1 + M + IL) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, N >= 0 a__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: mark(z) -{ 1 }-> a__zeros :|: z = 3 mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> a__length(a__zeros) :|: z = 1 + 3 mark(z) -{ 2 }-> a__length(a__take(mark(X16), mark(X26))) :|: X16 >= 0, X26 >= 0, z = 1 + (1 + X16 + X26) mark(z) -{ 2 }-> a__length(a__length(mark(X5))) :|: X5 >= 0, z = 1 + (1 + X5) mark(z) -{ 2 }-> a__length(a__and(mark(X15), X25)) :|: z = 1 + (1 + X15 + X25), X15 >= 0, X25 >= 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(X17) + X27) :|: z = 1 + (1 + X17 + X27), X17 >= 0, X27 >= 0 mark(z) -{ 2 }-> a__and(a__zeros, X2) :|: X2 >= 0, z = 1 + 3 + X2 mark(z) -{ 2 }-> a__and(a__take(mark(X13), mark(X23)), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 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(X12), X22), X2) :|: z = 1 + (1 + X12 + X22) + X2, X12 >= 0, X22 >= 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(X14) + X24, X2) :|: z = 1 + (1 + X14 + X24) + X2, X2 >= 0, X14 >= 0, X24 >= 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 ---------------------------------------- (263) 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 :|: ---------------------------------------- (264) 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__take(mark(X1''), mark(X2''))) :|: X1'' >= 0, X2'' >= 0, z = 1 + N + (1 + X1'' + X2''), 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) -{ 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(X11) + X21) :|: X11 >= 0, X21 >= 0, z = 1 + N + (1 + X11 + X21), N >= 0 a__length(z) -{ 3 }-> 1 + a__length(1 + 0 + 3) :|: z = 1 + N + 3, N >= 0 a__take(z, z') -{ 1 }-> 1 :|: z' = IL, z = 0, IL >= 0 a__take(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__take(z, z') -{ 1 }-> 1 + mark(N) + (1 + M + IL) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, N >= 0 a__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> a__length(a__take(mark(X16), mark(X26))) :|: X16 >= 0, X26 >= 0, z = 1 + (1 + X16 + X26) mark(z) -{ 2 }-> a__length(a__length(mark(X5))) :|: X5 >= 0, z = 1 + (1 + X5) mark(z) -{ 2 }-> a__length(a__and(mark(X15), X25)) :|: z = 1 + (1 + X15 + X25), X15 >= 0, X25 >= 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(X17) + X27) :|: z = 1 + (1 + X17 + X27), X17 >= 0, X27 >= 0 mark(z) -{ 3 }-> a__length(1 + 0 + 3) :|: z = 1 + 3 mark(z) -{ 2 }-> a__and(a__take(mark(X13), mark(X23)), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 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(X12), X22), X2) :|: z = 1 + (1 + X12 + X22) + X2, X12 >= 0, X22 >= 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(X14) + X24, X2) :|: z = 1 + (1 + X14 + X24) + X2, X2 >= 0, X14 >= 0, X24 >= 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 ---------------------------------------- (265) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (266) 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__take(mark(X1''), mark(X2''))) :|: X1'' >= 0, X2'' >= 0, z = 1 + N + (1 + X1'' + X2''), 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) -{ 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(X11) + X21) :|: X11 >= 0, X21 >= 0, z = 1 + N + (1 + X11 + X21), N >= 0 a__length(z) -{ 3 }-> 1 + a__length(1 + 0 + 3) :|: z - 4 >= 0 a__take(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0 a__take(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__take(z, z') -{ 1 }-> 1 + mark(N) + (1 + (z - 1) + IL) :|: z - 1 >= 0, IL >= 0, z' = 1 + N + IL, N >= 0 a__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> a__length(a__take(mark(X16), mark(X26))) :|: X16 >= 0, X26 >= 0, z = 1 + (1 + X16 + X26) mark(z) -{ 2 }-> a__length(a__length(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__length(a__and(mark(X15), X25)) :|: z = 1 + (1 + X15 + X25), X15 >= 0, X25 >= 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(X17) + X27) :|: z = 1 + (1 + X17 + X27), X17 >= 0, X27 >= 0 mark(z) -{ 3 }-> a__length(1 + 0 + 3) :|: z = 1 + 3 mark(z) -{ 2 }-> a__and(a__take(mark(X13), mark(X23)), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 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(X12), X22), X2) :|: z = 1 + (1 + X12 + X22) + X2, X12 >= 0, X22 >= 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(X14) + X24, X2) :|: z = 1 + (1 + X14 + X24) + X2, X2 >= 0, X14 >= 0, X24 >= 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 ---------------------------------------- (267) 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 ---------------------------------------- (268) 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] a__take(0, IL) -> nil [1] a__take(s(M), cons(N, IL)) -> cons(mark(N), take(M, IL)) [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(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [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] a__take(X1, X2) -> take(X1, X2) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:nil:s:take:and:length cons :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length 0 :: 0:zeros:cons:tt:nil:s:take:and:length zeros :: 0:zeros:cons:tt:nil:s:take:and:length a__and :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length tt :: 0:zeros:cons:tt:nil:s:take:and:length mark :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length a__length :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length nil :: 0:zeros:cons:tt:nil:s:take:and:length s :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length a__take :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length take :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length and :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length length :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length Rewrite Strategy: INNERMOST ---------------------------------------- (269) 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 ---------------------------------------- (270) 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__take(z, z') -{ 1 }-> 1 :|: z' = IL, z = 0, IL >= 0 a__take(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__take(z, z') -{ 1 }-> 1 + mark(N) + (1 + M + IL) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, N >= 0 a__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: mark(z) -{ 1 }-> a__zeros :|: z = 3 mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 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.